The document provides information about different number systems including decimal, binary, octal, and hexadecimal. It discusses the base and digits of each system. For binary, the base is 2 with digits 0 and 1. For octal, the base is 8 with digits 0-7. For hexadecimal, the base is 16 with digits 0-9 and A-F. It also describes how to convert between different number systems using tables and mathematical operations. For subtraction, it explains various complement methods used for each number system, such as 1's complement and 2's complement for binary, 7's/8's complement for octal, and 9's/10's complement for decimal. Finally, it discusses binary coded decimal (BCD)
The document provides an exam schedule for the week of July 19-24 listing the courses being tested each day. On Thursday, July 19 exams are scheduled for Computer Fundamentals and Physics lab. Friday has exams for English and Calculus. Monday's exam is for Humanities. Tuesday's exams are for PE and Sociology/Anthropology.
This document discusses 2's complement arithmetic in digital electronics. It explains that subtracting one number from another is the same as making one number negative and adding them. It then demonstrates how to represent negative numbers in binary by taking the 2's complement of a number, which involves complementing all its digits and adding 1. Various examples are provided of adding positive and negative binary numbers by taking the 2's complement of negative terms before adding. The most significant bit is identified as the sign bit that determines if a number is positive or negative.
This document discusses number representation and arithmetic operations in computers using binary numbers. It covers topics like positive and negative number representation using 1's and 2's complement, how addition and subtraction are performed in 2's complement, and concepts like carry and overflow that can occur. Examples are provided to illustrate how binary numbers are converted between decimal values and their 1's and 2's complement representations, and how arithmetic operations are performed on these binary numbers in 2's complement format.
Two's complement representation allows binary arithmetic on signed integers to yield the correct results. Positive numbers are represented as simple binary, while negative numbers are the binary complement of the corresponding positive number. The most significant bit indicates the sign, with 0 being positive and 1 being negative. To calculate the two's complement of a number, invert and add 1 to its binary representation. Two's complement arithmetic follows the same rules as binary arithmetic. Overflow occurs when adding two numbers of the same sign yields a result with the opposite sign.
1. Complements are used in digital computers to simplify subtraction and logical manipulations. 1's complement inverts all bits of a binary number. 2's complement inverts all bits and adds 1 to the least significant bit.
2. Subtraction using 1's complement involves taking the 1's complement of the subtrahend, adding it to the minuend, and handling any carry. Addition using 1's complements involves taking the complement of negative numbers before adding.
3. Subtraction using 2's complement involves taking the 2's complement of the subtrahend and adding it to the minuend. The result is negative if there is no carry out, and positive if there is a carry out.
1. Subtraction can be performed using addition by taking the complement of the subtrahend and adding it to the minuend.
2. The 1's complement of a binary number is obtained by flipping all bits, and 1's complement subtraction involves taking the complement of the smaller number and adding it to the larger number.
3. The 2's complement is obtained by adding 1 to the 1's complement, and 2's complement subtraction discards any carry when adding the 2's complement of the smaller number to the larger number.
This document discusses 1's and 2's complement in binary numbers. 1's complement involves flipping all the bits in a binary number to perform subtraction. 2's complement is obtained by adding 1 to the 1's complement. As an example, it shows subtracting 1010 from 1111 in binary using the 1's and 2's complement methods.
EC Binary Substraction using 1's Complement,2's ComplementAmberSinghal1
The binary number system represents all data as combinations of 0s and 1s. It is used in computer systems, where digits are combined to form binary numbers like 1001 or 11000110. A digit 0 or 1 in a binary number is called a bit. For example, 1001 is a 4-bit binary number and 11000110 is an 8-bit binary number. There are different methods for performing binary subtraction, including using 1's complement or 2's complement operations. With 1's complement subtraction, the bits of the number being subtracted are flipped before adding. With 2's complement subtraction, 1 is added to the 1's complement before adding.
The document provides an exam schedule for the week of July 19-24 listing the courses being tested each day. On Thursday, July 19 exams are scheduled for Computer Fundamentals and Physics lab. Friday has exams for English and Calculus. Monday's exam is for Humanities. Tuesday's exams are for PE and Sociology/Anthropology.
This document discusses 2's complement arithmetic in digital electronics. It explains that subtracting one number from another is the same as making one number negative and adding them. It then demonstrates how to represent negative numbers in binary by taking the 2's complement of a number, which involves complementing all its digits and adding 1. Various examples are provided of adding positive and negative binary numbers by taking the 2's complement of negative terms before adding. The most significant bit is identified as the sign bit that determines if a number is positive or negative.
This document discusses number representation and arithmetic operations in computers using binary numbers. It covers topics like positive and negative number representation using 1's and 2's complement, how addition and subtraction are performed in 2's complement, and concepts like carry and overflow that can occur. Examples are provided to illustrate how binary numbers are converted between decimal values and their 1's and 2's complement representations, and how arithmetic operations are performed on these binary numbers in 2's complement format.
Two's complement representation allows binary arithmetic on signed integers to yield the correct results. Positive numbers are represented as simple binary, while negative numbers are the binary complement of the corresponding positive number. The most significant bit indicates the sign, with 0 being positive and 1 being negative. To calculate the two's complement of a number, invert and add 1 to its binary representation. Two's complement arithmetic follows the same rules as binary arithmetic. Overflow occurs when adding two numbers of the same sign yields a result with the opposite sign.
1. Complements are used in digital computers to simplify subtraction and logical manipulations. 1's complement inverts all bits of a binary number. 2's complement inverts all bits and adds 1 to the least significant bit.
2. Subtraction using 1's complement involves taking the 1's complement of the subtrahend, adding it to the minuend, and handling any carry. Addition using 1's complements involves taking the complement of negative numbers before adding.
3. Subtraction using 2's complement involves taking the 2's complement of the subtrahend and adding it to the minuend. The result is negative if there is no carry out, and positive if there is a carry out.
1. Subtraction can be performed using addition by taking the complement of the subtrahend and adding it to the minuend.
2. The 1's complement of a binary number is obtained by flipping all bits, and 1's complement subtraction involves taking the complement of the smaller number and adding it to the larger number.
3. The 2's complement is obtained by adding 1 to the 1's complement, and 2's complement subtraction discards any carry when adding the 2's complement of the smaller number to the larger number.
This document discusses 1's and 2's complement in binary numbers. 1's complement involves flipping all the bits in a binary number to perform subtraction. 2's complement is obtained by adding 1 to the 1's complement. As an example, it shows subtracting 1010 from 1111 in binary using the 1's and 2's complement methods.
EC Binary Substraction using 1's Complement,2's ComplementAmberSinghal1
The binary number system represents all data as combinations of 0s and 1s. It is used in computer systems, where digits are combined to form binary numbers like 1001 or 11000110. A digit 0 or 1 in a binary number is called a bit. For example, 1001 is a 4-bit binary number and 11000110 is an 8-bit binary number. There are different methods for performing binary subtraction, including using 1's complement or 2's complement operations. With 1's complement subtraction, the bits of the number being subtracted are flipped before adding. With 2's complement subtraction, 1 is added to the 1's complement before adding.
1) Subtraction can be performed using addition by taking the complement of the number being subtracted.
2) For decimal numbers, the 10's complement is obtained by subtracting the number from 10^n where n is the number of digits.
3) Subtraction using complements involves taking the complement of the number being subtracted, adding it to the minuend, and optionally taking the complement of the sum depending on whether the minuend is greater than or less than the subtrahend.
This document discusses different types of number complements that allow subtraction to be performed using addition. It explains that subtraction using borrowing is inefficient for computers, so instead subtraction is done by taking the complement of one of the numbers and then adding. For binary numbers, the 2's complement is commonly used, where the 2's complement of a number is found by flipping all the bits and adding 1. The document provides examples of calculating 1's, 2's, and other bases' complements.
The document discusses various binary operations - addition, subtraction, multiplication, and division. It also covers 1's complement and 2's complement representations of signed binary numbers. Some key points covered include:
- Binary addition and subtraction use carry/borrow bits
- Multiplication is done by ANDing corresponding bits, division gives the quotient bit
- 1's complement is obtained by flipping all bits, 2's complement adds 1 to the 1's complement
- Subtraction can be performed using addition with 1's or 2's complement representations
- Signed numbers can be represented in sign-magnitude, 1's complement, or 2's complement forms.
The document discusses various binary number systems including binary addition, subtraction, multiplication and division, 1's and 2's complement representation of signed numbers, binary coded decimal, Gray code for error correction in digital communications, and excess-3 code which is a complementary BCD code where the equivalent decimal is converted by adding 3. Examples are provided to illustrate binary arithmetic operations and conversions between number systems.
1. Subtraction using 1's complement involves taking the complement of the subtrahend and adding it to the minuend. To subtract using 2's complement, take the 2's complement of the smaller number and add it to the larger number, omitting any carry.
2. The steps for 1's complement subtraction are: 1) take the 1's complement of the smaller number, 2) add it to the larger number, 3) add any carry to the result. For 2's complement, the steps are: 1) take the 2's complement of the smaller number, 2) add it to the larger number, omitting any carry.
3. The 2's complement is obtained by taking the 1
Binary arithmetic is essential for digital computers and systems. It involves adding, subtracting, multiplying, and dividing binary numbers using basic rules. Signed binary numbers represent positive and negative values using sign-magnitude, 1's complement, and 2's complement methods. Arithmetic operations on signed binary numbers follow rules for handling the sign bit and complement representations.
This document discusses different number systems including binary, octal, hexadecimal, and their arithmetic operations. It provides examples of adding and subtracting numbers in these systems. Binary addition follows four rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10. Octal addition is like decimal addition except when the column sum is greater than 7, 8 is subtracted and 1 is carried. Hexadecimal uses numbers 0-9 and letters A-F to represent values 10-15. It provides a table of decimal and hexadecimal equivalents. Hexadecimal addition involves treating multi-digit numbers as in decimal. Subtraction uses two's complement or 15's and 16's complement methods.
The document discusses different number systems including binary, denary, octal, and binary coded decimal. It explains that binary uses only two digits, 0 and 1, while denary uses ten digits from 0-9. Negative numbers are represented using sign-magnitude and two's complement in binary. Two's complement allows for arithmetic on negative binary numbers by treating the most significant bit as the sign and flipping all bits for the magnitude. The document also introduces octal which uses a base of 8 and binary coded decimal which represents each decimal digit with 4 binary digits.
The document discusses different methods for representing negative numbers in binary, including signed bit representation and two's complement representation. Two's complement is described as a better method as it avoids having two representations for zero. The key aspects of two's complement are explained, such as how to find the two's complement of a number by flipping its bits and adding one. Examples are provided to illustrate how negative numbers are represented using two's complement. The document also discusses the range of integers that can be stored using different numbers of bytes with two's complement representation.
Binary addition, Binary subtraction, Negative number representation, Subtraction using 1’s complement and 2’s complement, Binary multiplication and division, Arithmetic in octal, hexadecimal number system, BCD and Excess – 3 arithmetic
Binary coded decimal (BCD) is a numerical coding system that uses binary numbers to represent decimal digits. Each decimal digit from 0 to 9 is represented by a unique 4-bit binary code. BCD allows arithmetic operations like addition and subtraction on numbers. For BCD addition, the binary sum is calculated and if it exceeds 9, then 6 is added to obtain a valid BCD result. For BCD subtraction, the 9's complement of the subtrahend is calculated and added to the minuend, with carries propagated to the next group of bits.
The document discusses various methods for representing negative numbers in binary, including sign-and-magnitude, 1's complement, and 2's complement representations. It explains each method in detail, providing examples of how positive and negative numbers are represented. It also covers related topics like overflow, fixed-point versus floating-point number representations, and excess representation of exponents in floating-point numbers.
Contents:
1.What is number system?
2.Conversions of number from one radix to another
3.Complements (1's, 2's, 9's, 10's)
4.Binary Arithmetic ( Addition, subtraction, multiplication, division)
This document discusses different number systems and methods for calculating complements. It explains that there are two types of complements for each base-r system: the radix complement and the diminished radix complement. The diminished radix complement of a number N in base-r is defined as (r-1)n - N, where n is the number of digits in N. The radix complement is defined as rn - N. The document provides examples of calculating 1's, 2's, and other place value complements in binary and decimal number systems.
The document discusses different methods for representing integers and fractional numbers in binary, including sign and modulus representation, one's complement, two's complement, fixed point representation, and floating point representation. It provides examples and activities to help understand how to convert between decimal and binary representations using these methods.
This document summarizes key concepts in digital systems and binary numbers. It discusses why digital systems are preferred over analog, how to convert between number bases, signed and complement number representations, overflow, binary and decimal codes, BCD addition, Gray code, and parity checks. Digital systems are more cost effective, reliable, programmable and selective compared to analog. Number conversions involve grouping bits or dividing decimals. Signed number systems use complement representations to indicate positive and negative values.
Representation of Signed Numbers - R.D.SivakumarSivakumar R D .
This document discusses the representation of signed numbers in computers. It explains two common methods: sign-magnitude representation and 2's complement representation. For 2's complement, it provides the step-by-step process to convert a positive number to its negative equivalent in binary. It also discusses interpreting numbers as signed or unsigned and how this affects comparisons. Finally, it outlines the different value ranges for unsigned versus signed integers in an n-bit system.
The document discusses different methods for performing subtraction using addition of complements in digital logic design. It explains that subtraction by borrowing is difficult for digital computers, so subtraction is instead implemented by taking the complement of the numbers being subtracted and then adding them. Two types of complements are described: r's complement and r-1's complement. Examples of performing subtraction using complements in binary and decimal numbers are provided.
This document discusses digital electronics and number systems. It covers conversion between decimal, binary, octal and hexadecimal number bases. The key points covered include:
- Important number systems for digital systems are binary, octal and hexadecimal.
- Numbers in these systems use positional notation and can be represented as a power series expansion.
- Conversion between number bases can be done directly or by first converting to decimal.
- Binary addition and subtraction are performed digit-by-digit using logic gates.
- Binary multiplication is done by multiplying each bit of one number by the whole other number.
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
The document discusses different number systems including binary, octal, decimal, and hexadecimal. It provides details on their bases, the digits used in each system, and methods for converting between the different number systems. Conversions can be done directly between binary, octal, and hexadecimal without having to first convert to decimal.
1) Subtraction can be performed using addition by taking the complement of the number being subtracted.
2) For decimal numbers, the 10's complement is obtained by subtracting the number from 10^n where n is the number of digits.
3) Subtraction using complements involves taking the complement of the number being subtracted, adding it to the minuend, and optionally taking the complement of the sum depending on whether the minuend is greater than or less than the subtrahend.
This document discusses different types of number complements that allow subtraction to be performed using addition. It explains that subtraction using borrowing is inefficient for computers, so instead subtraction is done by taking the complement of one of the numbers and then adding. For binary numbers, the 2's complement is commonly used, where the 2's complement of a number is found by flipping all the bits and adding 1. The document provides examples of calculating 1's, 2's, and other bases' complements.
The document discusses various binary operations - addition, subtraction, multiplication, and division. It also covers 1's complement and 2's complement representations of signed binary numbers. Some key points covered include:
- Binary addition and subtraction use carry/borrow bits
- Multiplication is done by ANDing corresponding bits, division gives the quotient bit
- 1's complement is obtained by flipping all bits, 2's complement adds 1 to the 1's complement
- Subtraction can be performed using addition with 1's or 2's complement representations
- Signed numbers can be represented in sign-magnitude, 1's complement, or 2's complement forms.
The document discusses various binary number systems including binary addition, subtraction, multiplication and division, 1's and 2's complement representation of signed numbers, binary coded decimal, Gray code for error correction in digital communications, and excess-3 code which is a complementary BCD code where the equivalent decimal is converted by adding 3. Examples are provided to illustrate binary arithmetic operations and conversions between number systems.
1. Subtraction using 1's complement involves taking the complement of the subtrahend and adding it to the minuend. To subtract using 2's complement, take the 2's complement of the smaller number and add it to the larger number, omitting any carry.
2. The steps for 1's complement subtraction are: 1) take the 1's complement of the smaller number, 2) add it to the larger number, 3) add any carry to the result. For 2's complement, the steps are: 1) take the 2's complement of the smaller number, 2) add it to the larger number, omitting any carry.
3. The 2's complement is obtained by taking the 1
Binary arithmetic is essential for digital computers and systems. It involves adding, subtracting, multiplying, and dividing binary numbers using basic rules. Signed binary numbers represent positive and negative values using sign-magnitude, 1's complement, and 2's complement methods. Arithmetic operations on signed binary numbers follow rules for handling the sign bit and complement representations.
This document discusses different number systems including binary, octal, hexadecimal, and their arithmetic operations. It provides examples of adding and subtracting numbers in these systems. Binary addition follows four rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10. Octal addition is like decimal addition except when the column sum is greater than 7, 8 is subtracted and 1 is carried. Hexadecimal uses numbers 0-9 and letters A-F to represent values 10-15. It provides a table of decimal and hexadecimal equivalents. Hexadecimal addition involves treating multi-digit numbers as in decimal. Subtraction uses two's complement or 15's and 16's complement methods.
The document discusses different number systems including binary, denary, octal, and binary coded decimal. It explains that binary uses only two digits, 0 and 1, while denary uses ten digits from 0-9. Negative numbers are represented using sign-magnitude and two's complement in binary. Two's complement allows for arithmetic on negative binary numbers by treating the most significant bit as the sign and flipping all bits for the magnitude. The document also introduces octal which uses a base of 8 and binary coded decimal which represents each decimal digit with 4 binary digits.
The document discusses different methods for representing negative numbers in binary, including signed bit representation and two's complement representation. Two's complement is described as a better method as it avoids having two representations for zero. The key aspects of two's complement are explained, such as how to find the two's complement of a number by flipping its bits and adding one. Examples are provided to illustrate how negative numbers are represented using two's complement. The document also discusses the range of integers that can be stored using different numbers of bytes with two's complement representation.
Binary addition, Binary subtraction, Negative number representation, Subtraction using 1’s complement and 2’s complement, Binary multiplication and division, Arithmetic in octal, hexadecimal number system, BCD and Excess – 3 arithmetic
Binary coded decimal (BCD) is a numerical coding system that uses binary numbers to represent decimal digits. Each decimal digit from 0 to 9 is represented by a unique 4-bit binary code. BCD allows arithmetic operations like addition and subtraction on numbers. For BCD addition, the binary sum is calculated and if it exceeds 9, then 6 is added to obtain a valid BCD result. For BCD subtraction, the 9's complement of the subtrahend is calculated and added to the minuend, with carries propagated to the next group of bits.
The document discusses various methods for representing negative numbers in binary, including sign-and-magnitude, 1's complement, and 2's complement representations. It explains each method in detail, providing examples of how positive and negative numbers are represented. It also covers related topics like overflow, fixed-point versus floating-point number representations, and excess representation of exponents in floating-point numbers.
Contents:
1.What is number system?
2.Conversions of number from one radix to another
3.Complements (1's, 2's, 9's, 10's)
4.Binary Arithmetic ( Addition, subtraction, multiplication, division)
This document discusses different number systems and methods for calculating complements. It explains that there are two types of complements for each base-r system: the radix complement and the diminished radix complement. The diminished radix complement of a number N in base-r is defined as (r-1)n - N, where n is the number of digits in N. The radix complement is defined as rn - N. The document provides examples of calculating 1's, 2's, and other place value complements in binary and decimal number systems.
The document discusses different methods for representing integers and fractional numbers in binary, including sign and modulus representation, one's complement, two's complement, fixed point representation, and floating point representation. It provides examples and activities to help understand how to convert between decimal and binary representations using these methods.
This document summarizes key concepts in digital systems and binary numbers. It discusses why digital systems are preferred over analog, how to convert between number bases, signed and complement number representations, overflow, binary and decimal codes, BCD addition, Gray code, and parity checks. Digital systems are more cost effective, reliable, programmable and selective compared to analog. Number conversions involve grouping bits or dividing decimals. Signed number systems use complement representations to indicate positive and negative values.
Representation of Signed Numbers - R.D.SivakumarSivakumar R D .
This document discusses the representation of signed numbers in computers. It explains two common methods: sign-magnitude representation and 2's complement representation. For 2's complement, it provides the step-by-step process to convert a positive number to its negative equivalent in binary. It also discusses interpreting numbers as signed or unsigned and how this affects comparisons. Finally, it outlines the different value ranges for unsigned versus signed integers in an n-bit system.
The document discusses different methods for performing subtraction using addition of complements in digital logic design. It explains that subtraction by borrowing is difficult for digital computers, so subtraction is instead implemented by taking the complement of the numbers being subtracted and then adding them. Two types of complements are described: r's complement and r-1's complement. Examples of performing subtraction using complements in binary and decimal numbers are provided.
This document discusses digital electronics and number systems. It covers conversion between decimal, binary, octal and hexadecimal number bases. The key points covered include:
- Important number systems for digital systems are binary, octal and hexadecimal.
- Numbers in these systems use positional notation and can be represented as a power series expansion.
- Conversion between number bases can be done directly or by first converting to decimal.
- Binary addition and subtraction are performed digit-by-digit using logic gates.
- Binary multiplication is done by multiplying each bit of one number by the whole other number.
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
The document discusses different number systems including binary, octal, decimal, and hexadecimal. It provides details on their bases, the digits used in each system, and methods for converting between the different number systems. Conversions can be done directly between binary, octal, and hexadecimal without having to first convert to decimal.
This document discusses Newton's laws of motion and provides examples of forces. It introduces Newton's three laws, including inertia, Fnet=ma, and action-reaction. Examples are given for each law such as an astronaut drifting in space (1st law), graphs of force vs. acceleration (2nd law), and collisions between objects of different masses (3rd law). Common forces like gravity, tension, and normal forces are also explained.
The document discusses heat treatment processes for altering the mechanical properties of metals without changing their shape. It begins with an introduction to how a metal's microstructure and properties are dependent on its crystal structure and composition. It then defines heat treatment as the controlled heating and cooling of metals to achieve desired non-equilibrium structures and properties. The objectives of various heat treatments like softening, hardening, and stress relieving are described. Typical heat treatment cycles involving heating, holding, and controlled cooling are outlined. Time-temperature-transformation diagrams and continuous cooling transformation diagrams are introduced as tools for determining appropriate heat treatment parameters and expected microstructures. Factors affecting critical cooling rates and means of controlling grain size are also summarized.
- Decimal, binary, octal, and hexadecimal are different number systems used to represent numeric values.
- Decimal uses 10 digits (0-9), binary uses two digits (0-1), octal uses 8 digits (0-7), and hexadecimal uses 16 digits (0-9 and A-F).
- Each system has a base or radix - the number of unique digits used. Decimal is base 10, binary base 2, octal base 8, and hexadecimal base 16.
- Numbers can be converted between these systems using division and multiplication operations that take into account the place value of each digit based on the system's base.
3.3 Gas pressure & Atmospheric PressureNur Farizan
1) The document discusses gas and atmospheric pressure. It explains concepts like kinetic theory of gases, atmospheric pressure, units of measurement, and how pressure is affected by factors like altitude, temperature, and volume.
2) Various instruments for measuring pressure are described, including mercury barometers, aneroid barometers, manometers, and Bourdon gauges.
3) Applications of gas pressure are outlined, such as how straws, suckers, syringes, and vacuum cleaners work based on differences in air pressure.
4) Examples are provided to demonstrate calculating gas pressure values using given measurements from manometers and barometers.
1. The document discusses various heat treatment processes for steels including annealing, normalizing, and hardening.
2. Annealing involves heating and slow cooling to soften steel by refining grain structure. Types include stress relief, spheroidizing, and full annealing.
3. Normalizing refines grain size by heating above the critical temperature and slow cooling in air.
4. Hardening increases hardness and wear resistance by heating and quenching in water or oil to form martensite.
The document discusses various pressure measurement instruments such as pressure gauges, pressure switches, differential pressure gauges, and pressure transmitters. It describes the measuring principles, components, installation guidelines, and factors to consider when selecting pressure instruments for applications involving gases, liquids, and other process media. Proper instrument selection and installation is important to ensure accurate pressure measurement over the operating temperature and pressure ranges.
1. Pressure is force per unit area and is commonly measured in industries using pressure gauges. Common units include pascals, kilopascals, pounds per square inch, atmospheres, and bars.
2. Pressure gauges use elements like Bourdon tubes, diaphragms, or bellows to mechanically link pressure changes to a pointer that indicates the reading on a calibrated scale.
3. Factors like the process pressure and temperature, fluid properties, required accuracy, and installation conditions determine what type of pressure gauge element and accessories are suitable for an application.
This document discusses pressure measurement. It defines pressure as the force exerted by a fluid per unit area. Absolute pressure is measured with respect to zero pressure, while gauge pressure is absolute pressure minus atmospheric pressure. Pascal's Law states that pressure is equally distributed in all directions in a static fluid. Hydrostatic law relates pressure, depth, and fluid density. Manometry uses hydrostatic law to measure pressure by relating the height of a fluid column to pressure. Common pressure measurement instruments include piezometers, manometers, and pressure transducers such as capsules, bellows, bourdon tubes, and LVDT transducers, which convert pressure into mechanical movement.
The document provides an outline on heat treatment processes. It defines heat treatment and its purposes, discusses heat treatment theory and the stages of heat treatment including heating, soaking, and cooling. It describes various heat treatment processes like annealing, normalizing, hardening, and tempering. It also discusses case hardening techniques like carburizing, cyaniding, and nitriding. Finally, it introduces the TTT diagram and the microstructures obtained from different cooling rates.
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its a ppt based on the topic no. system.
it covers all the basics of ninth class cbse.
The document discusses computer number systems and data representation. It covers binary, octal, and hexadecimal number systems. It explains how computers use digital representation based on binary and how data is represented in memory as binary digits. It also discusses different data types, analog vs digital representation, and how various number systems are used to represent binary numbers.
This document discusses different number systems. It begins by explaining how early humans used basic counting systems before introducing concepts like zero, integers, rational and irrational numbers. It then defines different types of numbers like natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers. The rest of the document explains different base systems for representing numbers, including decimal, binary, octal and hexadecimal systems. It provides examples of converting between decimal and binary representations.
Friction. Do you know what is friction and how it plays different roles in our general life. There are many section in our life where friction is necessary like - in playing sitar and guitar, walking on the road and to hold something in our hand or in any mechanical devices. But there are many field where friction is not required like - in machines where two surfaces meet at a point. Due to this the life of the machine parts get decreased and failure may be occur there. Know more about different laws of friction, types of friction, elimination of the friction.
This document discusses various heat treatment processes used to harden gears, including through hardening, case hardening, and surface hardening. Case hardening involves processes like carburizing, nitriding, and carbo-nitriding to create a hard outer case and tough inner core. Surface hardening methods include induction hardening, which selectively heats parts of the gear, and flame hardening. The document provides details on how each process is performed and the advantages they provide for improving gear hardness, wear resistance, and fatigue life.
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Number System
Decimal Number System
Binary Number System
Why Binary?
Octal Number System
Hexadecimal Number System
Relationship between Hexadecimal, Octal, Decimal, and Binary
Number Conversions
The document discusses number systems. It begins by explaining how early humans counted items without a formal system by making marks or using objects to represent quantities. It then describes the development of number systems, starting with natural numbers, then extending to whole numbers with the inclusion of zero, and integers which allow for positive and negative numbers. Rational numbers are defined as any number that can be represented as a ratio of two integers. The key functions of learning number systems are outlined, including performing arithmetic operations on real numbers. Decimal representations of rational numbers are also discussed.
The document discusses various heat treatment processes including annealing, normalizing, quenching, and martensitic transformation. It provides details on the purposes, methods, and applications of each process. Annealing involves heating and slow cooling to relieve stresses and modify properties. Normalizing heats above the transformation temperature and air cools to produce a fine grain structure. Quenching rapidly cools steel above the transformation temperature to form very hard martensite. Martensitic transformation is the formation of acicular needlelike structures during rapid cooling of austenite.
This document discusses different number systems including binary, decimal, octal, and hexadecimal. It provides details on each system such as their number bases and allowed digits. The document also describes how to convert between these different number systems using methods like dividing numbers by the target base or grouping binary digits into sets of four for hexadecimal conversion. The goal is to understand representation of numbers in computing systems which commonly use binary and hexadecimal formats.
This document discusses different number systems used in digital computers and their conversions. It begins with an introduction to digital number systems and then describes the decimal, binary, octal and hexadecimal number systems. It explains how to represent integers and real numbers in binary. The document also covers number conversions between these systems using different methods like repeated division. Finally, it discusses various ways of representing integers in binary like sign-magnitude, one's complement and two's complement representations.
The document discusses number systems. It defines a number system as a system for writing and representing numbers using digits or symbols in a consistent manner. It allows for arithmetic operations and provides a unique representation for every number. The four most common number systems are decimal, binary, octal, and hexadecimal. Binary uses only two digits, 0 and 1, and is used to represent electrical signals in computers. Decimal uses base 10 with digits 0-9 in place values. [END SUMMARY]
The document discusses different number systems used in digital computers including binary, decimal, octal, and hexadecimal systems. It describes the characteristics of each system such as the base and digits used. Methods for converting between these different number systems are presented, including using division or grouping bits. The representation of signed integers as binary numbers is also covered, comparing sign-magnitude, one's complement, and two's complement representations. Binary addition is demonstrated with examples.
This document discusses different number systems used in computers such as binary, decimal, octal and hexadecimal. It provides examples of converting between these number systems. The key points are:
- Computers use the binary number system and understand numbers as sequences of 0s and 1s.
- Other common number systems include decimal, octal and hexadecimal, which use different bases.
- Methods for converting between number systems include dividing the number by the new base or using shortcuts that group digits in specific ways.
This document provides an overview of different number systems, including positional and non-positional systems. It describes the binary, decimal, octal, and hexadecimal systems, explaining their bases and symbols. Methods are presented for converting between these systems, such as using binary as an intermediary. Conversions include changing number values, as well as fractional representations. The objective is to understand number systems and perform conversions between binary, octal, decimal, and hexadecimal formats.
The binary number system and digital codes are fundamental to computers and to digital electronics in general. You will learn Binary addition, subtraction, multiplication, and Division.
Chapter 2.1 introduction to number systemISMT College
Binary Number System, Decimal Number System, Octal Number System, Hexadecimal Number System, Conversion, Binary Arithmetic, Signed Binary Number Representation, 1's complement, 2's complement, 9's complement, 10's complement
The document discusses different number systems including decimal, binary, octal, and hexadecimal. It provides examples and steps for converting between these number systems. The decimal system uses base 10, while binary uses base 2, octal uses base 8, and hexadecimal uses base 16. Computers commonly use binary, octal, and hexadecimal in addition to decimal. Conversion methods between the systems include division, multiplication, and treating digits as place values.
The document discusses different number systems including decimal, binary, hexadecimal, and octal number systems. It explains the basics of each system, such as the base and place value representation. It also covers how to perform operations like addition, subtraction, and conversion between the different number systems. Converting between binary and hexadecimal involves grouping bits into nibbles (4 bits) or nybbles (3 bits). Subtraction in computers is performed using two's complement by adding the complement of the subtrahend. Understanding number systems is important for computer science topics that involve binary, memory addresses, and color representation.
This document discusses different number systems including decimal, binary, octal, and hexadecimal. It provides information on how each system works including the base and valid digits used. Conversion methods between the different systems are also described, such as using repeated division to convert decimal to binary and multiplying place values to convert in the opposite direction. The relationships between the number systems are examined, like how each hexadecimal digit represents 4 binary digits.
This document discusses different numbering systems, including binary, decimal, octal, and hexadecimal. It explains how each system works using different bases and digits. The document also covers how to convert between these numbering systems, and how to perform basic arithmetic operations like addition and subtraction in binary.
The document discusses different number systems including binary, octal, decimal, and hexadecimal. It provides details on:
1) Converting between number systems using methods like the place value method or remainder method. For example, converting between binary, octal, and hexadecimal systems involves grouping bits or replacing digits with their base-n equivalents.
2) Representing negative numbers in binary, including through sign-magnitude and two's complement representations. The two's complement of a binary number is calculated by complementing each bit and adding 1.
3) Hexadecimal arithmetic which works similarly to decimal arithmetic but with 16 symbols (0-9 and A-F) instead of 10 symbols.
The document discusses different number systems used in computers such as binary, decimal, octal and hexadecimal. It provides examples and techniques for converting between these number systems. The key number systems covered are binary, which uses two digits (0 and 1), and is used in computers, decimal which uses 10 digits and is used in everyday life, octal which uses 8 digits, and hexadecimal which uses 16 digits and letters A-F. The document also discusses techniques for converting fractions between decimal and binary.
Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems comprise of multiple types based on the base value for its digits.
What is the Number Line?
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Positive Numbers: Numbers that are represented on the right side of the zero are termed as Positive Numbers. The value of these numbers increases on moving towards the right. Positive numbers are used for Addition between numbers. Example: 1, 2, 3, 4, …
Negative Numbers: Numbers that are represented on the left side of the zero are termed as Negative Numbers. The value of these numbers decreases on moving towards the left. Negative numbers are used for Subtraction between numbers. Example: -1, -2, -3, -4, …
Number and Its Types
A number is a value created by the combination of digits with the help of certain rules. These numbers are used to represent arithmetical quantities. A digit is a symbol from a set 10 symbols ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Any combination of digits represents a Number. The size of a Number depends on the count of digits that are used for its creation.
For Example: 123, 124, 0.345, -16, 73, 9, etc.
Types of Numbers
Numbers are of various types depending upon the patterns of digits that are used for their creation. Various symbols and rules are also applied on Numbers which classifies them into a variety of different types:
Number and Its Types
1. Natural Numbers: Natural Numbers are the most basic type of Numbers that range from 1 to infinity. These numbers are also called Positive Numbers or Counting Numbers. Natural Numbers are represented by the symbol N.
Example: 1, 2, 3, 4, 5, 6, 7, and so on.
2. Whole Numbers: Whole Numbers are basically the Natural Numbers, but they also include ‘zero’. Whole numbers are represented by the symbol W.
Example: 0, 1, 2, 3, 4, and so on.
3. Integers: Integers are the collection of Whole Numbers plus the negative values of the Natural Numbers. Integers do not include fraction numbers i.e. they can’t be written in a/b form. The range of Integers is from the Infinity at the Negative end and Infinity at the Positive end, including zero. Integers are represented by the symbol Z.
Example: ...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...
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1. Basic Electronics Notes
Number system
UNIT-VII
Syllabus
1. NUMBER SYSTEMS: Introduction, decimal system, Binary, Octal and Hexadecimal
number systems, addition and subtraction, fractional number, Binary Coded Decimal
numbers.
NUMBER SYSTEM
The human need to count things goes back to the dawn of civilization. To answer the
questions like how much or how many‖, people invented number system. A number system is
any scheme used to count things. The decimal number system succeeded because very large
numbers can be expressed using relatively short series of easily memorized numerals. Decimal or
base 10 number system‘s origin: can be traced to, counting on the fingers with digits. In any
number system, the important term is Base or radix
Base: Base is the number of different digits or symbols or numerals used to represent the number
system including zero in the number system. It is also called the radix of the number system.
Commonly used number systems :
1. Decimal
2. Binary
3. Octal
4. Hexadecimal.
Decimal number system :
The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4,
5, 6, 7, 8, 9. Using these symbols as digits of a number, we can express any quantity. The
decimal system is also called the base-10 system because it has 10 digits.
Binary number system :
In the binary system, there are only two symbols or possible digit values, 0 and 1. This base-2
system can be used to represent any quantity that can be represented in decimal or other base
system
Octal number system :
The octal number system has a base of eight, meaning that it has eight possible digits:
0,1,2,3,4,5,6,7. The octal numbering system includes eight base digits (0-7).After 7, the next
placeholder to the right begins with a “1”
i.e 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13 ...
Hexadecimal number system:
The hexadecimal system uses base 16. Thus, it has 16 possible digit symbols. It uses the digits 0
through 9 plus the letters A, B, C, D, E, and F ,to represent 10 through 16, as the 16 digit
symbols
Digits = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
Rohith.S, Asst. Professor, NCET, Bangalore
Page 1
2. Basic Electronics Notes
Number system
Conversion of number systems.
Converting from one number system to another is called conversion of number system or code
conversion, like converting from binary to decimal or converting from hexadecimal to decimal
etc.
Procedure for Conversion from One Number system to Other Number systems
Number
system Number
Procedure
(From)
system (To)
Multiply each bit by 2n, where n is the “weight” of the bit
Binary
Decimal
Hexadecimal
Add the results
Group every 4 bits and represent it into Hexadecimal using table
Group every 3 bit and Represent it into octal using table
Binary
Divide by two, keep track of the remainder
Group the remainders from Bottom to Top
Hexadecimal
Repeated division by 16 and Keep track of the Reminder.
Octal
Repeated division by 8 and Keep track of the Reminder.
Binary
Represent each digit by group of 3 bits as given in table
Decimal
Multiply each digit by 8n, where n is the “weight” of the bit
The weight is the position of the bit, starting from 0 on the right
Add the results
Convert Octal to Binary first.
Regroup the binary number by four bits per group starting from
LSB
Use the table to represent the digit
Binary
Represent each digit by group of 4 bits
Decimal
Multiply each bit by 16n, where n is the “weight” of the bit
The weight is the position of the bit, starting from 0 on the right
Add the results
Convert Hexadecimal to Binary first.
Regroup the binary number by three bits per group starting from
LSB.
Octal
Octal
Decimal
The weight is the position of the bit, starting from 0 on the right
Use the table to represent the digit
Hexadecimal
Hexadecimal
Octal
Rohith.S, Asst. Professor, NCET, Bangalore
Page 2
3. Basic Electronics Notes
Octal –To- Binary / Binary- To- Octal Conversion
Octal
0
1
2
3
Digit
Binary
000
001
010
011
Equivalent
Number system
4
5
6
7
100
101
110
111
5
6
7
0101
0110
0111
D
E
F
1101
1110
1111
Binary-To-Hexadecimal /Hexadecimal-To-Binary Conversion
Hexadecimal 0
1
2
3
4
Digit
Binary
0000
0001
0010
0011
0100
Equivalent
Hexadecimal 8
9
A
B
C
Digit
Binary
1000
1001
1010
1011
1100
Equivalent
Subtraction Using Number System
Complement method of subtraction
The complement method of subtraction is the method used for subtraction of numbers in
different number systems. This method is useful as it can easily implemented in arithmetic logic
circuits and inverting circuits in computers.
The complement method used in various no. systems discussed above is indicated below:
For decimal system – 9‘s complement method
– 10‘s complement method
For binary system
– 1‘s complement method
-- 2‘s complement method
For octal system
– 7‘s complement method
– 8‘s complement method
For hexadecimal system – 15‘s complement method
– 16‘s complement method
For subtraction of two numbers we have two cases :
1 Subtraction of smaller number from larger number
2 Subtraction of larger number from smaller number
Subtraction Using Binary no. System
The 1‘s complement of a given binary no. is the new no. obtained by changing all the 0‘
to 1, and all 0‘s to 1
Ex : 11010‘s 1‘s complement is 00101
Rohith.S, Asst. Professor, NCET, Bangalore
Page 3
4. Basic Electronics Notes
Number system
The 2‘s complement of a given binary no. is the new no. obtained by changing all the 0‘
to 1, and all 0‘s to 1 and then adding 1 to the least significant it
Ex : 11010‘s 2‘s complement is 1‘s complement 00101+1=00110
1’s complement method of subtraction
Subtraction of smaller number from larger number
1. Determine the 1‘s complement of the smaller no.
2. Add the first complement to the larger no.
3. Remove the carry and add it to the result. This is called end-around carry.
Subtraction of larger number from smaller number
1. Determine the first complement of the larger no.
2. Add the first complement to the smaller no.
3. Answer is in the 1‘s complement form. To get the answer in true form take the 1‘s
complement and assign –ve sign to the answer.
Advantages of 1’s complement method
1. The first complement subtraction can be accomplished with a binary adder. Therefore,
this method is useful in arithmetic logic circuits.
2. The first complement of a no. is easily obtained by inverting each bit in the no.
2’s complement method of subtraction
Subtraction of smaller number from larger number
1. Determine the 2‘s complement of a smaller no.
2. Add the 2‘s complement to the larger no.
3. Discard the carry.
Subtraction of larger number from smaller number
1. Determine the 2‘s complement of a larger no.
2. Add the 2‘s complement to the smaller no.
3. When there is no carry, answer is in the 2‘s complement form. To get the answer in
the true form take the 2‘s complement and assign –ve sign to the answer
Complement method of subtraction for octal number
7’s complement method of subtraction
The 7‘s complement of an octal no. is found by subtracting each digit from 7
Subtraction of smaller no. from larger no.
Step1 :Find 7‘s complement of subtrahend
Step2: Add two octal numbers (first no. and 7‘s complement of the second no.)
Step3 : I f the carry is produced in addition, add the carry to the least significant bit of the
sum, otherwise find 7‘s complement of the sum and attach –ve sign to it.
Rohith.S, Asst. Professor, NCET, Bangalore
Page 4
5. Basic Electronics Notes
Number system
Subtraction of larger number from smaller number
Step1 :Find 7‘s complement of subtrahend
Step2: Add two octal numbers (first no. and 7‘s complement of the second no.)
Step3 : I f the carry is not produced in addition then, find 7‘s complement of the sum as a
result and attach –ve sign to the result.
8’s complement method of subtraction
The 8‘s complement of an octal number is found by adding a 1 to the least significant bit of the
7‘s complement of an octal no.
Subtraction of smaller no. from larger no.
The steps for octal subtraction using 8‘s complement method are as given below
Step 1. Find 8‘s complement of subtrahend
Step 2 : Add two octal numbers (first no. and 8‘s complement of second no.)
Step 3 : If carry is produced in the addition, it is discarded., otherwise find 8‘s
complement of the sum as the result with –ve sign.
Subtraction of larger no. from smaller no.
Steps for Octal subtraction using 8‘s complement are as given below :
Step 1 : Find 8‘s complement of subtrahend
Step 2 : Add two Octal numbers (first no. and 8‘s complement of second no.)
Step 3 : If carry is produced in the addition, it is discarded, otherwise find 8‘s
complement of the sum as a result, with a –ve sign.
9’s complement method of subtraction
The 9‘s complement of a decimal no. is found by subtracting each digit from 9.
Subtraction of smaller no. from larger no.
Step 1 : Find 9‘s complement of subtrahend
Step 2 : Add two decimal numbers (first no. and 9‘s complement of second no.)
Step 3 : If carry is produced in the addition, add carry to the least significant bit of the
sum, otherwise find 9‘s complement of the sum as a result with a –ve sign.
Subtraction of larger no. from smaller no.
Step 1 : Find 9‘s complement of subtrahend
Step 2 : Add two hexadecimal numbers (first no. and 9‘s complement of second no.)
Step 3 : If carry is produced in the addition, add carry to the least significant bit of the
sum, otherwise find 9‘s complement of the sum and attach –ve sign to it.
10’s complement method of subtraction
The 10‘s complement of a Decimal no. is found by adding a 1 to the least significant bit of the
9‘s complement of a decimal no.
Subtraction of smaller no. from larger no.
Steps for Decimal subtraction using 10‘s complement are as given below :
Step 1 : Find 10‘s complement of subtrahend.
Step 2 : Add two decimal numbers (first no. and 10‘s complement of second no.)
Rohith.S, Asst. Professor, NCET, Bangalore
Page 5
6. Basic Electronics Notes
Number system
Step 3 : If carry is produced in the addition, it is discarded, otherwise find 10‘s
complement of the sum as a result, with a –ve sign.
Subtraction of larger no. from smaller no.
Steps for Decimal subtraction using 10‘s complement are as given below :
Step 1 : Find 10‘s complement of subtrahend
Step 2 : Add two Decimal numbers (first no. and 10‘s complement of second no.)
Step3 : If carry is produced in the addition, it is discarded, otherwise find 10‘s
complement of the sum as a result, with a –ve sign.
Complement method of subtraction for Hexadecimal number
15’s complement method of subtraction
The 15‘s complement of a hexadecimal no. is found by subtracting each digit from 15.
Subtraction of smaller no. from larger no.
Step 1 : Find 15‘s complement of subtrahend
Step 2 : Add two hexadecimal numbers (first no. and 15‘s complement of second no.)
Step 3 : If carry is produced in the addition, add carry to the least significant bit of the
sum, otherwise find 15‘s complement of the sum as a result with a –ve sign.
Subtraction of larger no. from smaller no.
Step 1 : Find 15‘s complement of subtrahend
Step 2 : Add two hexadecimal numbers (first no. and 15‘s complement of second no.)
Step 3 : If carry is produced in the addition, add carry to the least significant bit of the
sum, otherwise find 15‘s complement of the sum and attach –ve sign to it.
16’s complement method of subtraction
The 16‘s complement of a hexadecimal no. is found by adding a 1 to the least significant bit of
the 15‘s complement of a hexadecimal no.
Subtraction of smaller no. from larger no.
Steps for Hexadecimal subtraction using 16‘s complement are as given below :
Step 1 : Find 16‘s complement of subtrahend.
Step 2 : Add two hexadecimal numbers (first no. and 16‘s complement of second no.)
Step3 : If carry is produced in the addition, it is discarded, otherwise find 16‘s
complement of the sum as a result, with a –ve sign.
Subtraction of larger no. from smaller no.
Steps for Hexadecimal subtraction using 16‘s complement are as given below :
Step 1 : Find 16‘s complement of subtrahend
Step 2 : Add two hexadecimal numbers (first no. and 16‘s complement of second no.)
Step 3 : If carry is produced in the addition, it is discarded, otherwise find 16‘s
complement of the sum as a result, with a –ve sign
Binary Coded Decimal Numbers - BCD
Rohith.S, Asst. Professor, NCET, Bangalore
Page 6
7. Basic Electronics Notes
Number system
BCD is an abbreviation for binary coded decimal. BCD is a numeric code in which each digit
of a decimal number is represented by a separate group of bits. The most common BCD code is 8-42-1 BCD, in which each decimal digit is represented by a 4 bit binary number. It is called 8-4-2-1
BCD because the weights associated from right to left are 1-2-4-8.
The table below shows decimal digit and its corresponding code.
Decimal Number
Binary Number
(8421)
1
0001
2
3
0010
0011
4
5
0100
0101
6
0110
7
8
0111
1000
9
1001
The advantage of BCD is that it is easy to convert between it and decimal. The disadvantage
is the arithmetic operations are more complex when compared to binary.
BCD ADDITION
The addition of two BCD nos. can be best understood by considering the following three conditions :
Case1: The sum equals 9 or less with no carry
Case2: The sum equals greater than 9 with no carry
Case3: The sum equals 9 or less with a carry
Case1: The sum equals 9 or less with no carry
Take two numbers 6 and 3 in BCD and add
5 ----- 0101
4 ----- 0100
--------------------9 ----- 1001 The addition is carried out as in normal binary addition and the sum is 1001 which is a
BCD code for 9.
Case2: The sum equals greater than 9 with no carry
Let us consider addition of the numbers 6 and 8 in BCD
6 ----- 0110
8 ----- 1000
--------------------14 ---- 1110 invalid BCD number. This has occurred because the sum of the two digits
exceeds 9. In this case to correct the situation add 6 in BCD i.e 0110 to the invalid BCD no. as shown
below.
Rohith.S, Asst. Professor, NCET, Bangalore
Page 7
8. Basic Electronics Notes
Number system
6 ----- 0110
8 ----- 1000
--------------------14----- 1110
0110
----------------0001 0100
Observe that after addition of 6 a carry is produced into the second decimal position.
Case3: The sum equals 9 or less with a carry
Let us consider addition of the numbers 8 and 9 in BCD
8 ----- 1000
9 ------1001
--------------------17 0001 0001 In correct BCD No.
0110 Add 6 for correction
--------------------------0001 0111 BCD for 17
BCD Subtraction
A negative BCD no. can be expressed by taking 9‘s complement or 10‘s complement. The9‘s
complement of a decimal number is found by subtracting each digit in the number by 9.The 10‘s
complement is 9‘s complement +1.
Decimal
Number
0
1
2
3
4
5
6
7
8
9
9’s complement
9
8
7
6
5
4
3
2
1
0
10’s
complement
0
9
8
7
6
5
4
3
2
1
Subtraction as follows :
Find the 9‘s or 10‘s complement of a negative no.
Add the two numbers using BCD addition
If carry is generated add carry to the result treating it as end around carry, if it is 9‘s
complement subtraction, discard the carry if it is 10‘s complement. If there is no carry
generated take corresponding 9‘s or 10‘s complement of the result and attach –ve sign to the
result.
Rohith.S, Asst. Professor, NCET, Bangalore
Page 8