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

[cyenko]

Homework Statement

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.

Homework Equations

Overflow = C[SUB]n[/SUB] - C[SUB]n-1[/SUB]

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=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?

Thanks for your time,
Chris

 

[KataKoniK]

Hello Chris,

Thank you for your post. This is a challenging problem, but I believe there are a few different approaches you can take to solve it. Here are some suggestions that may help you get started:

1. Consider using a 4-bit adder instead of an 8-bit adder. Since you are only allowed to use one 8-bit adder, using a 4-bit adder would give you more flexibility in terms of routing the input bits and generating the overflow signal.

2. Use the MUXs to select which bits from the two 16-bit numbers will be fed into the adder. You can use the selector inputs of the MUXs to control this, and you may need to use multiple MUXs to select all the necessary bits.

3. To generate the overflow signal, you can use the carry-out (Cn) and carry-in (Cn-1) signals from the adder. These signals can be XORed to obtain the overflow signal, as you mentioned in your attempt.

4. Another approach would be to use a 16-bit adder/subtractor circuit instead of a single 8-bit adder. This would require more components, but it may be easier to implement.

I hope these suggestions are helpful. Good luck with your design! Let me know if you have any further questions.