Logic Gates

The Inverter The inverter (NOT circuit) performs the operation called inversion or complementation. Standard logic symbols: 1 1 input output input output

Inverter Truth Table & Logic Expression InputOutput LOW (0)HIGH (1) LOW (0) A X = A

The AND Gate & Its Operation The AND gate is composed of two or more inputs and a single output. For a 2-input AND gate:  Output X is HIGH only when inputs A and B are HIGH  X is LOW when either A or B is LOW, or when both A and B are LOW. & A B X A B X

AND Gate Truth Table The total number of possible combinations of binary inputs to a gate is determined by: N = 2 n Therefore:  2 bits (n=2) = 4 combinations  3 bits = 8 combinations  4 bits = 16 combinations INPUTSOUTPUT ABX A B X

AND Gate – Logic Expressions Use either:  X = A · B,or  X = AB If there are more than 2 inputs, do as below: A B X X= ABC X= ABCD A B C A B C D

The OR Gate Like AND gate, an OR gate has two or more inputs and one output. For a 2-input OR gate:  output X is HIGH when either input A or input B is HIGH, or when both A and B are HIGH.  X is LOW only when both A and B are LOW. A B X ≥ 1 A B X

OR Gate Truth Table INPUTSOUTPUT ABX A B X

OR Gate – Logic Expressions Use the operator + for OR operation  X = A + B  If there are more than 2 inputs, do as below: X= A+B+C X= A+B+C+D A B C A B C D

The NAND Gate NAND = NOT-AND For a 2-input NAND gate:  Output X is LOW only when inputs A and B are HIGH  X is HIGH when either A or B is LOW, or when both A and B are LOW & A B X A B X A B X

NAND Gate Truth Table & Logic Expression INPUTSOUTPUT ABX A B X The Boolean expression for the output of a 2- input NAND gate is X = AB

Negative-OR Equivalent Op of a NAND For a 2-input NAND gate performing a negative-OR operation  Output X is HIGH when either input A or input B is LOW or when both A and B are LOW NAND Negative-OR

The NOR Gate NOR = NOT-OR For a 2-input NOR gate:  Output X is LOW when either input A or input B is HIGH, or when both A and B are HIGH  X is HIGH only when both A and B are LOW A B X A B X ≥ 1 A B X

NOR Gate Truth Table & Logic Expression INPUTSOUTPUT ABX A B X The Boolean expression for the output of a 2- input NOR gate is X = A+B

Negative-AND Equivalent Op of a NOR For a 2-input NOR gate performing a negative-AND operation  Output X is HIGH only when both inputs A and B are LOW NOR Negative-AND

The XOR and XNOR Gates Exclusive-OR and Exclusive-NOR gates are formed by a combination of other gates already discussed. Because of their fundamental importance in many applications, these gates are often treated as basic logic elements with their own unique symbols.

The XOR Gate For a 2-input exclusive-OR gate:  Output X is HIGH when input A is LOW and input B is HIGH, or when input A is HIGH and input B is LOW  X is LOW when A and B are both HIGH and both LOW = 1 A B X A B X

XOR Gate Truth Table & Logic Expression INPUTSOUTPUT ABX A B X The Boolean expression for the output of a 2- input XOR gate is X = A+B

The XNOR Gate For a 2-input exclusive-NOR gate:  Output X is LOW when input A is LOW and input B is HIGH, or when input A is HIGH and input B is LOW  X is HIGH when A and B are both HIGH and both LOW = 1 A B X A B X

XNOR Gate Truth Table & Logic Expression INPUTSOUTPUT ABX A B X The Boolean expression for the output of a 2- input XNOR gate is X = A+B