Number system slide electronic device

1. NUMBER SYSTEM
BY.
ANUP BARMAN
Roll No. : L2023ECE08
Presentation submitted for CA1 examination
of the
Paper : Digital System Design(EC302)
Department Of ECE
Cooch Behar Government Engineering College

2. CONTENT
*Binary, Decimal,Octal and Hexadecimal Number System.
*Number Conversion

3. INTRODUCTION
The knowledge of numbers and the value it holds. A number system
helps to understand the position of every digit in every figure.A
number system denotes how we use numbers everywhere and make
use of them. A number system denotes which number sits where and
what value it possesses. Understanding the number system helps to
understand what bases do the number hold in a figure. A number
base is a key factor in understating the system. number base tells us
how many numbers are there while using a type of particular
numbering system.For instance, decimal means base 10 whereas
binary stands for base two. The decimal system denotes using from 0
to 9 digits, and binary uses 0 and 1. For a man’s uses, base 10 is
generally required for different purposes, while computed needs and
works with binary base.

4. BINARY NUMBERS
*Used to represent the voltage levels of a digital circuit.
*Only two voltage levels present in a digital circuit, logic High and logic Low.
*The high voltage is +5V and the low voltage is +0V.
*The binary numbers represent the logic low as a 0 and the logic high as a 1.

5. DECIMAL NUMBERS
*Electronics use decimals for accurate sensor reading.
*Devices convert continuous signals into decimal values.
*Decimal numbers are fundamental in coding for numerical
operations.
*Microcontrollers use decimal arithmetic for various device functions.

6. OCTAL NUMBERS
* Octal system uses digits 0-7 to represent numbers.
*Octal(base-8)
*Example: Show the conversion of a decimal number to octal (e.g., 15
in decimal is 17 in octal).

7. HEXADECIMAL NUMBERS
* Hexadecimal (Base-16)
* Hexadecimal system uses digits 0-9 and letters A-F to represent
numbers.
* illustrate the conversion of a decimal number to hexadecimal (e.g.,
31 in decimal is 1F in hexadecimal).
*Highlight the use of hexadecimal in programming and color
representation.

8. CONVERSION : DECIMAL TO
BINARY
•Note that the first remainder becomes the most significant bit (MSB). The last remainder becomes
the least significant bit (LSB).
•A Decimal number can be converted to a binary number by successful dividing the number by 2 as follows.

9. CONVERSION : BINARY TO
DECIMAL
 A binary number is converted to a decimal number by summing together the
weights of various positions in the binary number which contain a 1. For example,
10101112 = 8710.

10. CONVERSION : DECIMAL TO OCTAL
 A decimal number can be converted to an octal number by successively dividing
the number by 8 as follows:
266 ÷ 8 = 33 remainder 2 LSD (right-most digit)
33 ÷ 8 = 4 remainder 1
4 ÷ 8 = 0 remainder 4 MSB (left-most digit).
 Therefore 26610 = 4128

11. CONVERSION: OCTAL TO DECIMAL
 To convert an octal number to a decimal number, multiply each octal value by the
weight of the digit and sum the results. For example, 4128 = 26610.

12. CONVERSION : OCTAL TO BINARY
 Conversion from octal to binary is very straightforward. Each octal digit is replaced
by 3-bit binary number. For example, 4728 = 100 111 0102.
 A binary number is converted into an octal number by taking groups of
3 bits, starting from LSB, and replacing them with an octal digit. For
example, 11 010 1102 = 3268
.

13. CONVERSION : HEXADECIMAL TO
BINARY
 Each hex digit can be represented by a 4-bit binary number as shown above.
Conversion from hex to binary is very straightforward. Each hex digit is replaced by
4-bit binary number.
 A binary number is converted into an octal number by taking groups
of 4 bits, starting from LSB, and replacing them with a hex digit. For
example, 110101102 = 3268
.

14. CONCLUSION
mastering binary, decimal, octal, and hexadecimal number systems is
crucial for navigating the digital landscape. From the simplicity of
binary in computing to the versatility of hexadecimal in
programming, these systems play distinct roles in shaping our
technological world. Understanding them empowers us to
communicate effectively with computers and decode the language of
modern computing

15. REFERENCES
*URL: https://www.tutorialspoint.com/number-systems-in-digital-
electronics
*BOOK: DIGITAL NUMBER SYSTEM by K.GOKUL,
NUMBER SYSTEM by RAJNISH MISHRA