Data Structures

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This topic is an extension of the topic of Boolean Algebra which includes a more thorough description of the category in terms of determining whether a circuit results in a TRUE or FALSE value using truth tables or how to simplify a circuit to as few gates as possible. Electrical engineers use the following symbols to design electrical circuits that are used inside the computer’s hardware. The following table illustrates the equivalent Boolean algebra expression and truth table for each gate. NAME GRAPHICAL SYMBOL ALGEBRAIC EQUATION TRUTH TABLE


X = A A X 0 0 1 1

NOT

X = A X 0 1 1 0

AND X = AB or A*B A B X 0 0 0 0 1 0 1 0 0 1 1 1

NAND

X = or A B X 0 0 1 0 1 1 1 0 1 1 1 0

OR

X = A+B A B X 0 0 0 0 1 1 1 0 1 1 1 1

NOR

X = A B X 0 0 1 0 1 0 1 0 0 1 1 0

EXCLUSIVE-OR (XOR)

X = AB A B X 0 0 0 0 1 1 1 0 1 1 1 0

EQUIVALENCE (XNOR)

X = A B X 0 0 1 0 1 0 1 0 0 1 1 1