# Arithmetic Circuits & Full Adders

#### KongMD

1. The problem statement, all variables and given/known data
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 Xi and Yi for a single stage of the circuit given inputs A & B are n-bit registers.

2. Relevant equations

3. 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, Xi is often Ai. Why? Where do these variables come from??

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