logic circuit, electric circuit whose output depends upon the input in a way that can be expressed as a function in symbolic logic; it has one or more binary inputs (capable of assuming either of two states, e.g., "on" or "off") and a single binary output. Logic circuits that perform particular functions are called gates. Basic logic circuits include the AND gate, the OR gate, and the NOT gate, which perform the logical functions AND, OR, and NOT. Logic circuits can be built from any binary electric or electronic devices, including switches, relays, electron tubes, solid-state diodes, and transistors; the choice depends upon the application and design requirements. Modern technology has produced integrated logic circuits, modules that perform complex logical functions. A major use of logic circuits is in electronic digital computers. Fluid logic circuits have been developed whose function depends on the flow of a liquid or gas rather than on an electric current
POS (PRODUCT OF SUM)
Find the logic 0 outputs and invert those inputs in the product of sum format:
A | B | C | F |
0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 0 |
POS expression=(A+B+C)(A+B'+C)(A'+B'+C)(A'+B'+C')
SOP(SUM OF PRODUCT)
There are two commonly used techniques for deriving Boolean equations from a truth table. In the first technique, the minterms corresponding to each line in the truth table for which the output is logic 1 are extracted and combined using | OR operators. This method results in an equation said to be in the sum-of-products form. In the second technique, the maxterms corresponding to each line in the truth table for which the loutput is logic 0 are combined using & AND operators. This method results in an equation said to be in product-of-sums form.
A | B | C | F |
0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 0 |
SOP expression=A'B'C+A'BC+AB'C'+AB'C
MINTERM
For each combination of inputs to a logical fnction, there is an associated minterm.
A | B | C | Minterm |
0 | 0 | 0 | A'B'C' |
0 | 0 | 1 | A'B'C |
0 | 1 | 0 | A'BC' |
0 | 1 | 1 | A'BC |
1 | 0 | 0 | AB'C' |
1 | 0 | 1 | AB'C |
1 | 1 | 0 | ABC' |
1 | 1 | 1 | ABC |
MAXTERM
For each combination of inputs to a logical function, there is an associated maxterm.
A | B | C | Maxterm |
0 | 0 | 0 | A+B+C |
0 | 0 | 1 | A+B+C' |
0 | 1 | 0 | A+B'+C |
0 | 1 | 1 | A+B'+C' |
1 | 0 | 0 | A'+B+C |
1 | 0 | 1 | A'+B+C' |
1 | 1 | 0 | A'+B'+C |
1 | 1 | 1 | A'+B'+C' |
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