Logic NAND Gate
The Logic NAND Gate is a combination of the digital logic AND gate with that of an inverter or NOT gate connected together in series.
The NAND (Not – AND) gate has an output that is normally at logic level “1” and only goes “LOW” to logic level “0” when ALL of its inputs are at logic level “1”. The Logic NAND Gate is the reverse or “Complementary” form of the AND gate we have seen previously.Logic NAND Gate Equivalence
Then we can define the operation of a 2input digital logic NAND gate as being:
“If either A or B are NOT true, then Q is true”
Transistor NAND Gate
A simple 2input logic NAND gate can be constructed using RTL Resistortransistor switches connected together as shown below with the inputs connected directly to the transistor bases. Either transistor must be cutoff “OFF” for an output at Q.The Digital Logic “NAND” Gate
2input Logic NAND Gate
Symbol

Truth Table


2input
NAND Gate

B

A

Q

0

0

1


0

1

1


1

0

1


1

1

0


Boolean
Expression Q = A.B

Read as
A AND B gives NOT Q

3input Logic NAND Gate
Symbol

Truth Table


3input
NAND Gate

C

B

A

Q

0

0

0

1


0

0

1

1


0

1

0

1


0

1

1

1


1

0

0

1


1

0

1

1


1

1

0

1


1

1

1

0


Boolean
Expression Q = A.B.C

Read as
A AND B AND C gives NOT Q

A 4input NAND Function
If the number of inputs required is an odd number of inputs any “unused” inputs can be held HIGH by connecting them directly to the power supply using suitable “Pullup” resistors.
The Logic NAND Gate 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 = AB or A↑B.
The “Universal” NAND Gate
The Logic NAND Gate is generally classed as a “Universal” gate because it is one of the most commonly used logic gate types. NAND gates can also be used to produce any other type of logic gate function, and in practice the NAND gate forms the basis of most practical logic circuits. By connecting them together in various combinations the three basic gate types of AND, OR and NOT function can be formed using only NAND‘s, for example.Various Logic Gates using only NAND Gates
As well as the three common types above, ExOr, ExNor and standard NOR gates can be formed using just individual NAND gates.
Commonly available digital logic NAND gate IC’s include:
TTL Logic NAND Gates
 74LS00 Quad 2input
 74LS10 Triple 3input
 74LS20 Dual 4input
 74LS30 Single 8input
CMOS Logic NAND Gates
 CD4011 Quad 2input
 CD4023 Triple 3input
 CD4012 Dual 4input
7400 Quad 2input Logic NAND Gate
In the next tutorial about Digital Logic Gates, we will look at the digital logic NOR Gate function as used in both TTL and CMOS logic circuits as well as its Boolean Algebra definition and truth tables.