Combinatorial Logic Circuits
In order to design a logic circuit there are generally four basic steps involved, these are
- Choose the representation of the binary data states 0 (False) and 1 (True) for the electronic ciruit.
- Define the truth table for the circuit.
- Express the truth table in one of two alternative canonical forms. (see Canonical forms)
- Construct the circuit according to this Boolean expression.
Note that combinatorial logic circuits consist of an output that is independent of the input conditions as a function of time.
The representation of the binary data in the electronic cicuit is usually pre-defined according to some convention. Most modern-day circuits employ so-called positive coding whereby the binary state 1 or True is represented by +5 Volts and the binary state of zero is represented by 0 Volts.
The choice of coding is important however. Consider for example a circuit which behaves as the following truth table under positive coding
| A | B | Y |
|---|---|---|
| 0V | 0V | 0V |
| 0V | 5V | 0V |
| 5V | 0V | 0V |
| 5V | 5V | 5V |
by changing to negative coding, (+5V = 0 (False), 0V = 1 (True)) the truth table becomes
| A | B | Y |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 0 |
which is equivalent to the OR function.
It is important to recognise here that the circuit has not been changed, only the choice of the representation of the binary numbers. It is also important to note that in switching from positive coding to negative coding the circuit functionality has gone from AND to OR and not, as might be expected, from AND to NAND.
