Information sheet/Kertas Penerangan

INSTITUT KEMAHIRAN MARA BESUT
JALAN BATU TUMBUH, ALOR LINTANG,
22000 BESUT,
TERENGGANU DARUL IMAN.
INFORMATION SHEET
( KERTAS PENERANGAN )
PROGRAM’S CODE &
NAME/ KOD DAN NAMA
PROGRAM
EE-021-2:2012 INDUSTRIAL ELECTRONICS
LEVEL/ TAHAP L2
COMPETENCY UNIT NO.
AND TITLE/ NO. DAN
TAJUK UNIT
KOMPETENSI
C02 INSTRUMENT AND TEST EQUIPMENT SETUP &
HANDLING
WORK ACTIVITIES NO.
AND STATEMENT/ NO.
DAN PENYATAAN
AKTIVITI KERJA
1. IDENTIFY INSTRUMENT AND TEST EQUIPMENT
SET UP & HANDLING
2. PREPARE FOR INSTRUMENT AND TEST
EQUIPMENT SET UP & HANDLING
3. SET UP INSTRUMENT AND TEST EQUIPMENT
4. PERFORM RECORDING AND TAGGING OF
INSTRUMENT & TEST EQUIPMENT
5. REPORT INSTRUMENT AND TEST EQUIPMENT SET
UP & HANDLING
CODE NO. / NO. KOD EE-021-2:2012-C02/P(2/15)
Page/ Muka Surat: 1
Of / Drpd : 16
TITLE/ TAJUK:
NUMBER SYSTEMS IN DIGITAL
PURPOSE/ TUJUAN:
This information sheet purposes to explain details on number systems involved in digital
systems. The explanations related on binary number system, addition and subtraction
operations of binary number system including fractions and non-fractions, 1’s and 2’s
compliments of binary number and arithmetic operations and conversion of base in
numbering systems.

INFORMATION/ PENERANGAN:
The binary number system and digital codes are fundamental to computers and to
digital electronics in each general. In this chapter, the binary number and its
relationship to other number system such as decimal, hexadecimal and octal is
presented.
1. COUNT IN BINARY NUMBER SYSTEM
The binary number is simply another way to represent quantities. The binary
number system is less complicated than the decimal system because it has only
two digits. The two binary digits (bits) are I and 0. In a number system, this is
expressed as a base of 2. As with the decimal number system, each bit (digit)
position of a binary number carries a particular weight that determines the
magnitude of that number.
2. BINARY AND DECIMAL NUMBER CONVERSION
i. Convert From The Decimal Form To Binary Form – Without Fractions.
To convert from decimal to binary, use repeated division-by-2. For example, the
conversion of the decimal number I210 to binary by repeated division by 2.
Converting decimal number 12 to binary begin by dividing 12 by 2. Then divide
each resulting quotient by 2 until there is a 0 whole number quotient. The
reminder generates each division form the binary number. The first reminder to
be produced is the LSB (least significant bit) in the binary number and the last
reminder to be produced is the MSB (most significant bit).
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ii. Convert From The Decimal Form To Binary Form Involving Fractions.
Decimal fraction can be converted to binary by repeated multiplication-by-2. For
example, the conversion of the decimal number O.312510 to binary by repeated
multiplication by 2. Converting the decimal fraction 0.312510 to binary, begin by
multiplying 0.3125 by 2 and then multiplying each resulting fractional part of the
product by 2 until the fractional product is zero or until the desired number of
decimal places is reached. The carried digits, or carries generated by the
multiplications produce the binary number. The first carry produced is the MSB and
the last carry is the LSB.
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iii. Convert From The Binary Form To Decimal Form.
The decimal value of any binary number can be found by adding the weights of all
bits that are I and discarding the weight of all bits that are 0. For an example the
conversion of the binary number 11011012 to decimal number as below:
iv. Convert From The Binary Form To Decimal Form Including Fractions.
Example the conversion of the binary fraction number 0.10112 to decimal number is
as below:
3. ADD AND SUBTRACT BINARY NUMBERS INCLUDING FRACTIONS
i. Addition Operation.
The four basic rules for adding two binary digits (bits) are as follows.
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Example: Compute the addition operation of the binary number 1012 and 102
Example: Add the binary number 10102 and 112
Example: Add the binary number 110102 and 11002
ii. Subtraction Operation.
The four basic rules for subtracting bits are as follows.
Example: Subtract the binary number 10102 from 100012
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4. 1’s AND 2’s COMPLIMENTS OF BINARY NUMBER
The 1’s and 2’s compliment of binary numbers are important because they permit
the representation of negative (-ve) numbers.
i. 1’s Compliment.
The 1’s compliment of a binary is found by changing all 1’s to 0s and all 0s to 1s. In
other words, change each of bits in the number to its complement. The operation is
compute as examples shown below.
Example: Find the 1’s compliment of
10110010
00011010
ii. 2’s Compliment.
The 2’s complement of a binary number is formed by taking the 1’s complement of
the number and adding 1 to the least significant bit (LSB) position.
10111000
00010110
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5. EXPRESS SIGNED NUMBERS IN BINARY FORM
The left - most bit in a signed binary number is the sign bit, which tells you whether
the number is positive or negative. A 0 sign bit indicates a positive number, and a 1
sign bit indicates a negative number.
i. Sign Magnitude Form.
When a signed binary number is represented in sign - magnitude, the left - most bits
is the sign bit and the remaining bits are the magnitude bits. The magnitude bits are
in true (un-complemented) binary for both positive and negative numbers.
For example, the decimal number +25 is expressed as an 8-bits signed number
using the sign-magnitude form as shown below.
The decimal number -25 is expressed as 1 0 0 1 1 0 0 1. Notice that the only
difference between +25 and -25 is the sign bit because the magnitude bits are in
true binary for both positive and negative numbers. In the sign-magnitude form, a
negative number has the same magnitude bits as the corresponding positive
number but the sign bit is a 1 rather than zero.
ii. 1’s Complement Form.
Positive numbers in l’s complement form are represented the same way as the
positive sign-magnitude numbers. Negative numbers, however, are the 1’s
complements of the corresponding positive numbers. For example, using eight bits,
the decimal number -25 is expressed as the 1’s complement of +25 (00011001) as
11100110. In the 1’s complement form, a negative number is the 1’s complement of
the corresponding positive number.
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iii. 2’s Complement Form.
Positive numbers in 2’s complement form are represented the same way as in the
sign-magnitude and 1’s complement forms. Negative numbers are the 2’s
complements of the corresponding positive numbers.
Example: Express decimal number -25 as 2’s complement.
In the 2’s complement form, a negative number is the 2’s complement of the
corresponding positive number.
Example: Express the decimal number -39 as an 8 bit number in the sign-
magnitude, 1’s complement and 2’s complement forms.
+39 = 00100111
In the sign-magnitude form -39 = 10100111
 In 1‘s complement form -39,
 In 2 ‘s complement form -39,
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6. ARITHMETIC OPERATIONS WITH SIGNED NUMBERS
In this topic you will learn how signed numbers are added, subtracted, multiplied
and divided. Because the 2’s complement form for representing signed numbers is
the most widely used in computers and microprocessor-based systems, the
coverage in this topic is limited to 2’s complement arithmetic.
i. Addition In 2’s Complement System.
Let’s take one case at a time using 8-bit signed numbers as examples.
• CASE 1: Two positive numbers. Add +7 with +4.
• CASE 2: Positive number and smaller negative number. Add +15 with -6.
• CASE 3: Positive number and larger negative number. Add +16 with -24.
• CASE 4: Two negative number. Add -5 with -9.
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• CASE 5: Equal and opposite number. Add -9 with +9.
ii. Subtraction In 2’s Complement System.
Negate the subtrahend - will change the subtrahend to its equivalent value of
opposite sign while adding the negation to the minuend - the result will represent the
difference in between the subtrahend and minuend. Discard any final carry bit.
Example: Perform each of the following subtractions of the signed numbers.
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7. CONVERSION OF BASE IN NUMBERING SYSTEMS
i. Octal to Binary Conversion.
Because each octal digit can be represented by a 3-bit binary number, it is very
easy to convert from octal to binary. Each octal digit is represented by three bits as
shown below.
Example: Convert each of the following octal numbers to binary.
a) 138 b) 258 c) 1408 d) 72568
ii. Binary to Octal Conversion.
Example: Convert each of the following binary numbers to octal.
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iii. Binary to Hexadecimal Conversion.
The hexadecimal number system has sixteen digits and is used primarily as a
compact way of displaying or writing binary numbers because it is very easy to
convert between binary and hexadecimal.
Hexadecimal is widely used in computer and microprocessor application. The
hexadecimal number system has of sixteen; that is it is composed of 16 digits and
alphabetic characters. Most digital systems process binary data in groups that are
multiples of four bits, making the hexadecimal number very convenient because
each hexadecimal digit represents a 4-bit binary number as listed below.
DECIMAL BINARY HEXADECIMAL
0 0 0 0 0 0
1 0 0 0 1 1
2 0 0 1 0 2
3 0 0 1 1 3
4 0 1 0 0 4
5 0 1 0 1 5
6 0 1 1 0 6
7 0 1 1 1 7
8 1 0 0 0 8
9 1 0 0 1 9
10 1 0 1 0 A
11 1 0 1 1 B
12 1 1 0 0 C
13 1 1 0 1 D
14 1 1 1 0 E
15 1 1 1 1 F
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Example: Convert the following binary numbers to hexadecimal.
iv. Hexadecimal to Binary Conversion.
Example: Determine the binary numbers for the following hexadecimal numbers.
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QUESTION/ SOALAN:
Answer all the questions.
1. Compute the following operation.
2. Determine the positional value of 7 of the following.
i. 17 = ________________________________________
ii. 70 = ________________________________________
iii. 117 = ________________________________________
iv. 276 = ________________________________________
v. 8794 = ________________________________________
3. Compute the following sign-magnitude operations.
i. (-11) + (-23).
ii. (+3) + (-7).
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2 X 101
+ 8 X 100
=

4. Convert each of the following base to decimal.
i. 10012 = _____________________
ii. A16 = _____________________
iii. 4F16 = _____________________
iv. 01012 = _____________________
v. 138 = _____________________
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REFERENCE/RUJUKAN:
1. Ronald J. Tocci (Fifth Edition, 2008). Prentice Hall International., Digital System
– Principle and Application. Pages : 132 till 150.
2. Tocci., Widmer., Moss (Tenth Edition, 2013). Pearson International Edition.,
Digital System – Principle and Application. Pages : 115 till 135.
3. Floyd (Ninth Edition, 2010). Pearson Prentice Hall., Digital Fundamental. Pages :
145 till 163.
4. Nigel P. Cook (2010). Prentice Hall., Introductory Digital Electronic. Pages : 112
till 125.
5. William Kleitz (Fifth Edition, 2011)., Prentice Hall., Digital Electronics – A
practical Approach. Pages : 110 till 132.
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