Incompletely Specified Logic Functions (Don’t Cares)
Situations can arise where a circuit has N input signals, but not all
Input combinations that cannot possibly effect the proper operation of a logic system can be allowed to drive circuit outputs high or low‚ literally, the designer doesn’t care what the circuit response is to these impossible or irrelevant inputs. This information is encoded by using a special‚ don’t care‚ symbol in truth tables and K-maps to indicate that the signal can be a ‘1’ or a ‘0’ without effecting circuit operation. Some sources use an ‘X’ to indicate a don’t care, but this can be confused with a signal named ‘X’. It is perhaps a better practice to use a symbol that is not normally associated with signal names‚ here, we choose the
The truth table above shows two output functions (F and G) for the same three inputs. Both outputs have two rows where the output is a don’t care. This same information is also shown in the associated K-maps. In the ‘F’ K-map, the designers‚ “don’t care"‚ if the output is a ‘1’ or a ‘0’ for minterms 2 and 7, and so cells 2 and 7 in the K-map can be looped as either a ‘1’ or a ‘0’. Clearly, looping cell 7 as a ‘1’ and cell 2 as a ‘0’ results in a more minimal logic circuit. In this case, both an SOP and POS looping would result in identical circuits.
In the ‘G’ K-map, the don’t cares in cells 1 and 3 can be looped as either a ‘1’ or a ‘0’. In an SOP looping, both don’t cares would be looped as 1’s, giving a logic function of
- If all combination of
inputs are possible, some combinations may be irrelevant.
- Some combinations of input signals can be completely inconsequential to the operation of the circuit.
- It is possible to take advantage of the situations where input combinations are not required for the function of the circuit to further minimize the logic circuit.
- Information for the irrelevant inputs are noted by the
symbol and are known as Don’t Cares.