Chapter 2.1, Problem 2.10PP

Program Plan Intro

Boolean algebra operations:

• The Boolean algebra is represented by the two element set such as {0, 1}.
  • Encode logic value for “1” and “0” is “TRUE” and “FALSE” respectively.
• Operation of Boolean algebra are “~”, “&”, “|” and “^”.
  • Encode logical operations for “~”, “&”, “|” and “^” is “NOT”, “AND”, “OR”, and “EXCLUSIVE-OR” respectively.

Boolean operation “^”:

This Boolean operation is used to “EXCLUSIVE-OR” of two bits vectors.

• This Boolean operation is represented by “^”.

^	0	1
0	0	1
1	1	0

The “EXCLUSIVE-OR” operation satisfies the two properties such as “commutative property” and “associative property”.

• Commutative property:
  • This property is used to reverse the variables order without modifying the fact of the equation.
  • The example for commutative property is shown below:

For addition: $\text{X}\text{+}\text{Y}\text{=}\text{Y}\text{+}\text{X}$

For multiplication: $\text{XY}\text{=}\text{YX}$

• Associative property:
  • This property is used to associate the groups of variables with parentheses without modifying the fact of the equation.
  • The example for associative property is shown below:

$\text{X}\left(\text{YZ}\right)\text{=}\left(\text{XY}\right)\text{Z}$