# Implement a Boolean function using 4 to 1 multiplexer

#### mcc123pa

Joined Sep 12, 2010
40
Hi again-

Here are the instructions to the second problem that I am wondering about:

A combinational circuit is specified by the following Boolean function:
F(A,B,C,D)= Ʃ(0,2,6,7,8)
Implement the circuit using ONE 4:1 multiplexer and other necessary gates. Use A and B as MUX selection inputs. Only uncomplemented inputs are available.

My attempt at a solution is as follows:
A B C D F
0 0 0 0 1
0 0 0 1 0
0 0 1 0 1
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 1
0 1 1 1 1
1 0 0 0 1
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0

Above is my truth table. The problem should be fairly simple only I am confused of how to set it up with the directions saying I should only use uncomplemented inputs. That is because I got D0 = D' and D2= C'D'. How should I procede to get the correct answer? Thanks in advance for your help!

#### blah2222

Joined May 3, 2010
582
Hi again-

Here are the instructions to the second problem that I am wondering about:

A combinational circuit is specified by the following Boolean function:
F(A,B,C,D)= Ʃ(0,2,6,7,8)
Implement the circuit using ONE 4:1 multiplexer and other necessary gates. Use A and B as MUX selection inputs. Only uncomplemented inputs are available.
F = A'B'C'D' + A'B'CD' + A'BCD' + A'BCD + AB'C'D'

Use Shannon's Expansion to factor out select inputs:

F = A[B'C'D'] + A'[B'C'D' + B'CD' + BCD' + BCD]
F = A[B(0) + B'(C'D')] + A'[B(CD' + CD) + B'(C'D' + CD')]

Tidying it up:

F = A[B(0) + B'(C'D')] + A'[B(C) + B'(D')]

Rich (BB code):
            AB
||
D' -------->|\
C  -------->| \
C'D' ------>| |-------->F
0  -------->| /
|/

Last edited:

#### Georacer

Joined Nov 25, 2009
5,181
What the instruction said is that you don't have the inputs complement ready to use and you have to use an inverter to obtain it.
No big deal.