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Chapter: Digital Principles and System Design - Boolean Algebra and Logic Gates

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Arithmetic Operations

Binary Equivalents, Binary Addition, Rules of Binary Subtraction

ARITHMETIC OPERATIONS


Binary Equivalents

 

1        Nybble (or nibble)  =  4 bits 1 Byte  =  2 nibbles  =  8 bits

1        Kilobyte (KB)  =  1024 bytes 

1        Megabyte (MB)    =  1024 kilobytes =  1,048,576 bytes

1        Gigabyte (GB)      =  1024 megabytes         =  1,073,741,824 bytes


ü Binary Addition


ü    Rules of Binary Addition


Note: The  rules of binary addition (without carries) are the same as the truths of the  XOR gate.

 

ü Binary Subtraction


ü    Rules of  Binary Subtraction

 

·                         0 -  0 = 0

·                         0 -  1 = 1, and borrow 1 from the next more significant bit

·                         1 -  0 = 1

·                         1 -  1 = 0

 

ü Example

 

00100101 - 00010001= 00010100


 

ü Binary Multiplication

 

ü    Rules of Binary Multiplication

 

·                         0 x 0 = 0

·                         0 x 1 = 0

 

·                         1 x 0 = 0

·                         1 x 1 = 1, and no carry or borrow bits

 

ü     Example

 


Note: The rules of binary multiplication are the same as the truths of the AND gate.

ü Binary Division

 

Binary division is the repeated process of subtraction, just as in decimal division.

 

ü     Example 1:  00101010 ÷ 00000110 = 00000111


 

Example 2: 10000111 ÷ 00000101 = 00011011 1.3 1.4 1.5


 

 

Ref: 1) John F. Wakerly, “Digital Design Principles and Practices”, Fourth Edition, Pearson Education 2007. Pg.No:35-44.

2)  Morris  Mano  M.  and  Michael  D.  Ciletti,  “Digital  Design”,  IV  Edition,  Pearson  Education Pg.No:9-14.

 


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