Given the Boolean function F(A, B, C, D) = π(0, 1, 3, 5, 6, 7, 9, 11, 13, 14, 15). Reduce the above expression by using 4-variable Karnaugh map, showing…

Computer Science20235 marksCase basedBoolean AlgebraTool: Boolean algebra solver

Reduce the following using a Karnaugh map.

Given the Boolean function F(A, B, C, D) = π(0, 1, 3, 5, 6, 7, 9, 11, 13, 14, 15). Reduce the above…

Given the Boolean function $F(A, B, C, D) = \pi(0, 1, 3, 5, 6, 7, 9, 11, 13, 14, 15)$.

(a)[4]

Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).

(b)[1]

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Draw: Logic gate diagram for the reduced expression

Must show: variables and their complements as inputs

Open in the Boolean algebra solver

Answer

Answer (a)

Groups: (1, 3, 5, 7, 9, 11, 13, 15) → D'; (6, 7, 14, 15) → (B' + C'); (0, 1) → (A + B + C)

Reduced expression: F = D'(B' + C')(A + B + C)

Grouping the 0s: octet {1,3,5,7,9,11,13,15} = D', quad {6,7,14,15} = (B' + C'), pair {0,1} = (A + B + C).

Answer (b)

Logic gate diagram for $F=(A+B+C)\cdot(B'+C')\cdot D'$: a 3-input OR gate (A, B, C) and a 2-input OR gate (B', C') feed a 3-input AND gate together with D'.