Arithmetic Circuits & Full Adders

[KongMD]

Homework Statement

An arithmetic circuit has two select lines S₁ and S₂ and does the following arithmetic operations using a full adder:

[function table]

Determine the simplified Boolean functions for X_i and Y_i for a single stage of the circuit given inputs A & B are n-bit registers.

Homework Equations

The Attempt at a Solution

All I want to know is how to turn the given function table into a truth table so I can construct the logic diagram. Is the Carry-in part of the table? If so, that would make this question a 5x5, which is something we've never done (columns for S1, S0, Ai, Bi, Cin). This stuff is so confusing - sorry that I can't articulate better.

Other questions: Looking at my notes for a similar exercise, X_i is often A_i. Why? Where do these variables come from??

 

[lewando]

[function table]

Are you going to provide this?