The 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
The Logic NAND Function only produces and 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
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 | ||
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.
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.
The Logic NOR Function
Like the NAND Gate above, the NOR or
Not OR Gate is also a combination of two separate functions, the OR
function and the NOT function connected together in series and is expressed by the Boolean
expression as, A + B
The Logic NOR Function only produces and output when "ALL" of its inputs
are not present and in Boolean Algebra terms the output will be TRUE only when all
of its inputs are FALSE.
Switch Representation of the NOR Function
The truth table for the NOR function is the opposite of that for the previous OR function because the NOR gate performs the reverse operation of the OR gate. Then we can see that the NOR gate is the complement of the OR gate.
NOR Function Truth Table
| Switch A | Switch B | Output | Description |
| 0 | 0 | 1 | Both A and B are open, lamp ON |
| 0 | 1 | 0 | A is open and B is closed, lamp OFF |
| 1 | 0 | 0 | A is closed and B is open, lamp OFF |
| 1 | 1 | 0 | A is closed and B is closed, lamp OFF |
| Boolean Expression (A OR B) | A + B | ||
The NOR Function is sometimes known as the Pierce Function and is denoted by a downwards arrow operator as shown, A NOR B = A↓B.
NOR Gates are available as standard i.c. packages such as the TTL 74LS02
Quadruple 2-input NOR Gate, the TTL 74LS27 Triple 3-input NOR Gate
or the 74LS260 Dual 5-input NOR Gate.
0 comments:
Post a Comment