# Implement a Boolean function using 4 to 1 multiplexer

Discussion in 'Homework Help' started by mcc123pa, Dec 5, 2010.

1. ### mcc123pa Thread Starter Member

Sep 12, 2010
40
0
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!

2. ### blah2222 Well-Known Member

May 3, 2010
565
33
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')]

Code ( (Unknown Language)):
1.             AB
2.             ||
3. D' -------->|\
4. C  -------->| \
5. C'D' ------>| |-------->F
6. 0  -------->| /
7.             |/

Last edited: Dec 6, 2010
3. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
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.

4. ### mcc123pa Thread Starter Member

Sep 12, 2010
40
0
Thanks for the help everyone!! I really appreciate it!!