# How to choose which function to use depending on the parameter value? (MUX and Gates implementation)

Let's say we have A,B,C , which are all representation of decimal numbers. A and C are 4bit, B is 2bit.

• if A is any of those numbers (eg: 0,5,6,11 ), the function is

F(A,B,C) = AB+C

• If A is the rest of the numbers , the function is :

F(A,B,C) = B+C

We can use 2x1 MUX, 2input logic gates (both as much as needed), and of course FA .

I tried to treat the numbers as minterms, and use K-map for A3A2A1A0. Where is the 2to1 MUX involved? How exactly should I choose how to operate based on the value of the numbers?

I don't have issues as to how to implement/use the adder (for additions and/or multiplications).I don't need any answer there/ I have troubles understanding :

1. How to treat the actual numbers (as minterms?)

2. Because in the second function, basically the A is missing, and it is an actual multiplication, is it wise to treat it as 1? . B+C is still 1B+C in mathematics. Right?

3. Should I represent every number with gates from scratch, no K-Map needed? What about the MUX?

4. Since I will need each bit separately ,as an input to the adder, then, should I , somehow, implement the 2to1 MUX to each specific bit?

$$(\overline {A3} + \overline {A2})(\overline {A3} + {A1})........$$