1. May 13, 2012

### cyenko

1. The problem statement, all variables and given/known data

Suppose we have only one 8-bit ripple carry adder but need to do 16-bit addition and subtraction.
Design a sequential circuit (FSM) with only one 8-bit ripple carry adder to implement a 16-bit adder-subtractor.
You are allowed to use MUXs and need to generate the overﬂow signal.

2. Relevant equations

Code (Text):
Overflow = C[SUB]n[/SUB] - C[SUB]n-1[/SUB]

3. The attempt at a solution

I've attempted to find similar circuit schematics, boolean expressions, diagrams, etc. online to no avail. I am familiar with the implementation with an 8-bit ripple carry adder, and can obtain the final overflow signal through

Code (Text):
O=C[SUB]7[/SUB] XOR C[SUB]6[/SUB]
Since I am prohibited from using two 8-bit adders, I was thinking of encoding the given 16 bit numbers using a 16-4 encoder, and then doing the operations, but this would not be valid when multiple bits of the given 16-bit numbers are set high.

I'm looking for guidance on where to begin. I think once I have the general idea on how 16 bits can be stuck in the 8 bit adder, I'll be able to do this problem. Specifically, where should I route the overflow to, and what combination of bits from the two original numbers should I put into the adder?

Chris