Logic NAND Function

The NAND or “Not AND” function is a combination of the two separate logical functions, the AND function and the NOT function connected together in series.

The logic NAND function can be expressed by the Boolean expression of, A.B

2-input logic gate


2-input NAND gate


The Logic NAND Function only produces an output when “ANY” of its inputs are not present and in Boolean Algebra terms the output will be TRUE only when any of its inputs are FALSE.

Switch Representation of the NAND Function

logic NAND gate


The truth table for the NAND function is the opposite of that for the previous AND function because the NAND gate performs the reverse operation of the AND gate. In other words, the NAND gate is the complement of the basic AND gate.

NAND Function Truth Table

Switch A Switch B Output Description
0 0 1 A and B are both open, lamp ON
0 1 1 A is open and B is closed, lamp ON
1 0 1 A is closed and B is open, lamp ON
1 1 0 A is closed and B is closed, lamp OFF
Boolean Expression (A AND B) A . B

logic nand function


The NAND Function is sometimes known as the Sheffer Stroke Function and is denoted by a vertical bar or upwards arrow operator, for example, A NAND B = A|B or A↑B.

Logic NAND gates are used as the basic “building blocks” to construct other logic gate functions and are available in standard i.c. packages such as the very common TTL 74LS00 Quadruple 2-input NAND Gates, the TTL 74LS10 Triple 3-input NAND Gates or the 74LS20 Dual 4-input NAND Gates. There is even a single chip 74LS30 8-input NAND Gate.


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