# 16-bit addition/subtraction with an 8-bit adder

by cyenko
Tags: 16bit, 8bit, adder
 P: 4 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 Overflow = Cn - Cn-1 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 O=C7 XOR C6 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? Thanks for your time, Chris