Engineering Arithmetic Circuits & Full Adders

AI Thread Summary
The discussion focuses on understanding how to convert a function table into a truth table for an arithmetic circuit using a full adder. The user expresses confusion about whether the Carry-in (Cin) should be included, suggesting a 5x5 table structure that includes select lines and inputs. There is also a query regarding the relationship between variables, specifically why Xi is often represented as Ai in similar exercises. The user seeks clarification on these concepts to aid in constructing the logic diagram. Overall, the thread highlights the challenges of working with Boolean functions and truth tables in circuit design.
KongMD
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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 Xi and Yi 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, Xi is often Ai. Why? Where do these variables come from??
 
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[function table]

Are you going to provide this?
 

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