# Multiplexers, expressions

#### power13

Joined Oct 23, 2018
8
Hello everyone,

I am trying to design a circuit.

F(a,b,c) = ab +c (if a=0,2,5,7,8)
F(a,b,c) = b +c (if a≠0,2,5,7,8)
a,c are 4bit binary numbers, b: 2bit number

I have to use multiplexers 2by1, full adders and logic gates.

I am trying to find a solution for the first part.
f1 = ab (if a...)..
f1: 6 bits
Karnaugh map for 6 bits I think is overkill. Is there any way to check the "a" with multiplexers?

Thank you.

#### WBahn

Joined Mar 31, 2012
27,372
So as "ab+c" a logical expression or an arithmetic expression?

#### power13

Joined Oct 23, 2018
8
It's arithmetic expression. It produces a number from multiplication and adder (using full adders, multiplexers 2by1 and logic gates).

#### WBahn

Joined Mar 31, 2012
27,372
So forget, for the moment, about the conditional component, how would you implement

f = a·b + c

using full adders and knowing that 'b' is a 2-bit value?

#### power13

Joined Oct 23, 2018
8
I think that I need 4 full adders for a·b and 6 full adders for the "+".

I don't know how to handle the conditional component.

#### WBahn

Joined Mar 31, 2012
27,372
I think that I need 4 full adders for a·b and 6 full adders for the "+".

I don't know how to handle the conditional component.
Draw out your circuit for the a·b+c circuit. You need a starting point, so start with that.

Can you make a logic function that is a 1 when the condition is met and a 0 otherwise?

#### power13

Joined Oct 23, 2018
8
a·b+c, a cursory circuit: https://i.postimg.cc/hjDQgW4f/2akalo.jpg

For the condition, I can use Karnaugh map to have a logic function. But I'm trying to find a way to use multiplexers 2by1 for this.

#### WBahn

Joined Mar 31, 2012
27,372
a·b+c, a cursory circuit: https://i.postimg.cc/hjDQgW4f/2akalo.jpg

For the condition, I can use Karnaugh map to have a logic function. But I'm trying to find a way to use multiplexers 2by1 for this.
Why do you want to use multiplexers for this part of the logic?

However you implement it, once you have a logic signal for the conditional part, how could you use a multiplexer to choose between the value of 'a' and '0001'? Would a mux really be the best choice here? Is there a simpler way?