Test: K-Map Simplification - Electrical Engineering (EE) MCQ

K-map is simply a rearranged truth table. It is a pictorial representation of truth table having a specific number of cells or squares, where each cell represents a Maxterm or a Minterm.

If A and B are the input for AND gate the output is obtained as AB and after inversion we get (AB)’, which is the expression of NAND gate. NAND gate produces high output when any of the input is 0 and produces low output when all inputs are 1.

The systematic reduction of logic circuits is accomplished by using boolean algebra.

Each “0” entry in a K-map square represents a LOW output for all possible HIGH input conditions. Thus, it represents Maxterm.

Looping on a K-map always results in the elimination of variables within the loop that appear in both complemented and uncomplemented form.

The commutative law of multiplication is (A * B) = (B * A).
The commutative law of addition is (A + B) = (B + A).

DeMorgan’s Law: ~(P+Q) <=> (~P).(~Q) Also,
~(P.Q) <=> (~P)+(~Q).

Each “1” entry in a K-map square represents a HIGH for each input truth table condition that produces a HIGH output. Thus, it represents a minterm.

The two BEST methods of logic circuit simplification are Boolean algebra and Karnaugh mapping. Boolean Algebra uses the Laws of Boolean Algebra for minimization of Boolean expressions while Karnaugh Map is a pictorial representation and reduction of the Boolean expression.

Sum of product means that it is the sum of all product terms. Thus, the number is multiplied first and then it is added: A * B + C * D.