University:
San Jose State University
Course:
EE 270 | Advanced Logic Design
Academic year:

2022
Views:

394

Pages:

2
Author:

Luciano Kirby

Modulo 2 Arithmetic Modulo 2 arithmetic is performed digit by digit on binary numbers. Each digit is considered independently from its neighbours. Numbers are not carried or borrowed. Addition/Subtraction Modulo 2 addition/subtraction is performed using an exclusive OR (xor) operation on the corresponding binary digits of each operand. 0 ± 0 = 0; 0 ± 1 = 1; 1 ± 0 = 1; 1±1=0 Multiplication 1011 x 0101 _________ 1011 0000 1011 0000 __________ 0100111 Division Modulo 2 division can be performed in a manner similar to arithmetic long division. Subtract the denominator (the bottom number) from the leading parts of the enumerator (the top number). Proceed along the enumerator until its end is reached. Remember that we are using modulo 2 subtraction. For example, we can divide 100100110 by 10011 as follows: 10001 remainder 101 10011|100100110 10011 10110 10011 101 This has the effect that X/Y = Y/X. For example: 1 remainder 1010 11001|10011 11001 1010 1 remainder 1010 10011|11001 9/22/2009 8:31 AM 10011 1010 9/22/2009 8:31 AM

Modulo 2 Arithmetic

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