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# Logic gates

The fundamental property of any statement is either True or False. The truth-value of any statement is the truthfulness or falsity of that statement.

Boolean algebra is a means for expressing the relationship between a logic circuits inputs and outputs. Two values 0’s and 1’s are the possible values in Boolean algebra.

Meaning of Truth Table

A truth table is a means for describing how logic circuit’s output depends on the logic level present at the circuit’s input.

Types of Logic Gates

The principal or five types of logical operators are (a) OR gate (b) AND gate (c) NOT (Inverter) gate (d) NOR gate (e) NAND.

1. OR gate

The OR gate gets its name from the fact that it behaves after the fashion of the logical inclusive ‘or.’ The output is “true” if either or both of the inputs are “true.” If both inputs are “false,” then the output is “false.”

Logic gates – NOT logic gateOR gate symbol

Truth Table of ‘OR’ Gate

INPUT ( a ) INPUT ( b ) OUTPUT (a + b)

0        0        0

0        1        1

1        0        1

1        1        1

1. AND gate

The AND gate is so named because, if 0 is called “false” and 1 is called “true”, the gate acts in the same way as the logical “and” operator. The following illustration and table show the circuit symbol and logic combinations for an AND gate. (In the symbol, the input terminals are at left and the output terminal is at right.) The output is “true” when both inputs are “true”. Otherwise, the output is “false”.

Logic gates – AND logic gateAND gate symbol

Truth Table of ‘AND’ Gate

INPUT ( a ) INPUT ( b ) OUTPUT (a * b)

0        0        0

0        1        0

1        0        0

1        1        1

1. NOT gate

A logical inverter sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. It reverses the logic state.

Logic gates – NOT logic gateNOT gate symbol

Truth Table for ‘NOT’ Gate

INPUT (a)   OUTPUT (a¯)

0        1

1        0

1. NOR gate

The NOR gate is a combination of OR gate followed by an inverter. Its output is “true” if both inputs are “false”. Otherwise, the output is “false”.

Logic gates – NOR logic gateNOR gate symbol

Truth Table for ‘NOR’ Gate

INPUT        INPUT        OUTPUT (OR)     OUTPUT (NOR)

X       Y       X+Y  (X+Y¯¯¯¯¯¯¯¯¯¯¯¯¯¯)

0        0        0        1

0        1        1        0

1        0        1        0

1        1        1        0

1. NAND Gate

The NAND gate operates as an AND gate followed by a NOT gate. It acts in the manner of the logical operation “and” followed by negation. The output is “false” if both inputs are “true”. Otherwise, the output is “true”.

Logic gates – NAND logic gateNAND gate symbol

Truth Table for ‘NAND’ Gate

INPUT        INPUT        OUTPUT (AND)  OUTPUT (NAND)

X       Y       X.Y   (X.Y¯¯¯¯¯¯¯¯¯¯)

0        0        0        1

0        1        0        1

1        0        0        1

1        1        1        0

EVALUATION

Define logic gate.

Define truth table.

List and explain the types of logic gates