Digital Logic Systems

Digital Logic Systems Combinational Circuits

Basic Gates & Truth Tables

Basic Gates AND Gate OR Gate NOT Gate

More Gates NAND Gate NOR Gate BUF Gate

More Gates XOR Gate XNOR Gate

3-Input XOR Gate 4-Input OR Gate n-Input Gates 5-Input NOR Gate 5-Input AND Gate

Definitions It gives a logical output true only if all the inputs are true AND It gives a logical output true if any of the inputs is true OR It gives a logical output true only if an odd-number of inputs is true XOR It gives a logical output true if the input is false and vice versa NOT

A truth table is a tabular procedure to express the relationship of the outputs to the inputs of a Logical System Truth Table

NOT Operation AND Operation OR Operation Truth Tables for Gates AND Gate OR Gate NOT Gate

BUF Operation NAND Operation NOR Operation Truth Tables for Gates NAND Gate NOR Gate BUF Gate

XOROperation XNOR Operation Truth Tables for Gates XOR Gate XNOR Gate

Bubbles A Bubble Implies a Logical Inversion Bubbles can be replaced by NOT Gates to get logically equivalent circuits

Generate tables for all combinations of bubbles and a XOR gate

Gate Equivalence = = =

Gate Equivalence = ? =

Gate Equivalence = =

Switching Expressions

Basic Switching Expressions f = a . b AND f = a + b OR f = a’ f = ā NOT

Is there an expression for XOR operation?

Switching Expressions f1 = a . b’ f2 = (a + b)’

Switching Expressions f = ?

Switching Expressions f = m + n m = a . b’ n = a’ . b

Switching Expressions f = (a . b’) + (a’ . b) This is the equivalent circuit and equivalent expression for a XOR operation

From Digital Design, 5th Edition by M. Morris Mano and Michael Ciletti

Switching Expressions f1 = a . b f2 = a ^ b f2 = (a . b’) + (a’ . b)

s = s c = m + g

s = p ^ z s = s m = p . z c = m + g g = g

Digital Logic Systems