BINARY FUNCTIONS
In order to attain high reliability in accuracy, the signals in electronic digital systems have only two discrete values (O or 1, high or low), and thus, the signals are binary variables. The cause-action relationships of a bistate switching circuit are limited to a smaIl number of possibilities. Consequendy, it is convenient to show the functional relationship between one or more independent binary input variables and the dependent binary output variable in tabular form (caIled a truth tab/e).
There are only two possible cases for processing of a single input signal A (independent variable) by a bistate switching circuit to yield output x = bı (A):
Case I : x =b11(A) = A, or the signal remains in the state that it occupied when entering the circuit (circuit known as a buffer).
Case II: x = b12(A) = A (read as A NOT or A complement), or the signal exits the bistate switching circuit in the opposite state from which it entered. Such a circuit is caIled an inverter. Tables 1 and 2 display the truth tables of the buffer and the inverter,respectively.
Table 1. X= b11(A)
Table 2. x = b12(A) ,
More general bistate circuits process two input binary variables (A and B) to produce a single binary output,
X = b2(A, B). Since there are two inputs, each of which could be one of two states, there are 22 = 4 possible combinations of input variables to form output x. The resulting truth table is shown by Table 3 where each Xi could be a 0 or 1
.
Referring to Table 3, there are four possible outputs from each two-input, one-output binary
A |
B |
X |
O |
O |
xı |
O |
1 |
X2 |
i |
O |
X3 |
1 |
1 |
X4 |
Table 3.X= b2(A, B)
logic circuit (logic gates). Since there are two possible states for each Xi (i = 1,2,3,4), a total of 24 = 16 possible output combinations are possible. Out of these sixteen possible logic circuits, only six find a significant use:
- AND
- OR
- NAND
- NOR
- EXOR
- EXNOR
and one more gate, The NOT gate.