Question

use logism: For each of the following functions, simplify using Karnaugh Maps, then build, and hand in a properlydocumented circuit. You need to submit both a K-Map as well as the circuit for each part. a) F1 (a,b,c,d) = Σ(1, 2, 3, 4, 5, 9,10,11) b) F2 (a,b,c,d) = Σ(2, 3, 4, 6, 8, 11, 15) δ(a,b,c,d) = Σ(0, 5, 7, 9, 10)

Answer 1

a)

The given function is :

F1 (a,b,c,d) = Σ(1, 2, 3, 4, 5, 9,10,11)

The Kmap for the given function is :

There is only one quad and 2 pairs.

Quad1 = b ' d

Pair1 = a ' b ' c

Pair2 = a ' b c '

The simplified expression for F1 ( a,b,c,d) is :

F1 = b ' d +   a ' b ' c +  a ' b c ' = b ' d + a ' ( b XOR c ).

The circuit diagram using logism is :

In the above figure, if the values of a, b, c and d are 0, 0, 1 and 0, then the output will be 1 that is true.

b)

The given function is :

F2 (a,b,c,d) = Σ(2, 3, 4, 6, 8, 11, 15)

The don't care function is :

δ(a,b,c,d) = Σ(0, 5, 7, 9, 10)

The Kmap for the given function is :

Here, x represents a don't care value.

There are 4 quads.

Quad1 = c d

Quad2 = a ' c

Quad3 = a ' b

Quad4 = a b '

The simplified expression for F2 ( a,b,c,d) is :

F2 = c d +  a ' c + a ' b +  a b ' = c ( d + a ' ) + ( a XOR b ).

The circuit diagram using logism is :

In the above figure, if the values of a, b, c and d are 0, 1, 0 and 0, then the output will be 1 that is true.