This document is a chapter on arithmetic operations in binary and hexadecimal number systems. It covers objectives which are to perform addition, subtraction, and explain terms like 1's complement, 2's complement, bit, nibble, byte and word. The chapter then shows examples of addition, subtraction, multiplication and division in binary, and explains 1's complement, 2's complement and why 2's complement is commonly used in computing.

1. IT2001PA
Engineering Essentials (2/2)
Chapter 2 – Arithmetic Operation
Lecturer Name
lecturer_email@ite.edu.sg
Nov 20, 2012
Contact Number

2. Chapter 2 – Arithmetic Operation
Lesson Objectives
Upon completion of this topic, you should be able to:
 Compute addition and subtraction arithmetic operation
for the binary and hexadecimal number systems.
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3. Chapter 2 – Arithmetic Operation
Specific Objectives
Students should be able to :
 Perform addition, subtraction using the binary and hexadecimal
number systems.
 Explain the use of :
 1’s complement of a binary number and
 2’s complement of a binary number.
 Explain the following terms :
 Bit
 Nibble
 Byte and
 Word.
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4. Chapter 2 – Arithmetic Operation
Binary addition
Add 0112 and 1102
011 (3)
+ 110 (6)
(1) carry
1001 (9)
Add 10010.012 and 111.102
10010.01 (18.25)
+ 111.10 ( 7.50)
(1) (1) carry
11001.11 (25.75)
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5. Chapter 2 – Arithmetic Operation
Binary Subtraction
Subtract 1112 from 11002
borrow (2) (1) (2)
1 1 0 0 (12)
- 1 1 1 ( 7)
1 0 1 ( 5)
Binary Subtraction of 10000.012 - 111.102
(1) (1) (1) (1) (2)
borrow
10000.01 (16.25)
- 111.10 ( 7.50)
1000.11 ( 8.75)
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6. Chapter 2 – Arithmetic Operation
Multiplication of Binary Numbers
1 0 0 12 ( 9)
x 1 0 1 12 (11)
1001
1001
0000
+1 0 0 1
(1) (1)
carry
1100011 (99)
( 64 32 0 0 0 2 1 binary )
6 5 1 0
22 22
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7. Chapter 2 – Arithmetic Operation
Binary division
10012 ÷ 112 (9 ÷ 3 = 3)
0011
(1) (2) borrow
11 1001
011
0011
0011
0000
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8. Chapter 2 – Arithmetic Operation
1’s complement
Bit by Bit inversion of a binary number.
Given: 110101112
Result of 1’s complement is 0 0 1 0 1 0 0 0 2
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9. Chapter 2 – Arithmetic Operation
2’s complement
Result of 1’s complement plus 1.
Given: 110101112
Result of 1’s complement is 0 0 1 0 1 0 0 0 2
+ 12
Result of 2’s complement is 0 0 1 0 1 0 0 1 2
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10. Chapter 2 – Arithmetic Operation
Why use 2’s complement
In computers, the operations of
subtraction can be performed using
only the addition operation with the
2’s complement method.
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11. Chapter 2 – Arithmetic Operation
Why 2’s complement is popular
This method is popular because
 only adder circuits are needed
 thus simplifying the circuitry.
Easy with digital circuits to get the
complements.
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12. Chapter 2 – Arithmetic Operation
Binary System
 Each digit in the binary number system is called a
bit
 A group of four bits binary number is known as
Nibble.
 A group of eight bits binary number is known as
Byte.
 Two bytes number form a word.
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13. Chapter 2 – Arithmetic Operation
Bit
A binary digit, e.g.: 0 or 1
Nibble
A group of 4 bits, e.g.: 1010
Byte
A group of 8 bits, e.g.: 1001 1011
Word
A group of 16 bits, e.g.: 1011 1010 1100 1001
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14. Chapter 2 – Arithmetic Operation
Next Lesson
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