Arithmetic Operations

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.