# Comparator design using a 4-bit adder

## Homework Statement

Hi, it's me again.
Now I am going to design a 4-bit magnitude comparator using just ONE 4-bit adder and infinitely large number of gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) for signed numbers (negative binary).

## Homework Equations

A > B => A3barB3 + A2barB2x3 + A1barB1x3x2 + A0barB0x3x2x1

similar for A < B and A = B.

## The Attempt at a Solution

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This is my attempt. Frankly, this is my first time encountering problems related to comparator design because this is never said to be in the syllabus of the course (introductory course). I find this in a past paper... seemingly indicating that the instructor wants us to divide and conquer it within the 3 hours of exam.

I do this all by resources on the internet. So there may be a lot of mistakes.

Svein
I think you are on the right track, but I have some comments:
• Where is the Cin coming from? You are only comparing two 4-bit numbers!
• Are the numbers supposed to be in two's complement?
And - there are only 16 combinations possible. I suggest making a truth table before continuing.

I think it should be using 2's complement.

Svein
I think it should be using 2's complement.
Then get busy on your truth table.

A truth table looks like this? because I have never drawn a truth table for such a design...so I searched on google...

#### Attachments

• Table_de_verite_du_CI_7485.gif
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I have a question about the XOR gates. Are those XOR gates for doing 2's complement (i am thinking in this way)?
But I know that 2's complement is not just inverting 1 and 0, but also needs to add 1 after that. It seems that the above design cannot do that?

And you mentioned that there should not be Cin? Does this mean there are no cascading inputs?

Svein