Comparator design using a 4-bit adder

[ichabodgrant]

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 C_in 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.

 

[ichabodgrant]

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.

 

[ichabodgrant]

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

 

[ichabodgrant]

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?

 

[ichabodgrant]

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

 

[Svein]

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

No. I meant the truth table for what you are trying to design. Since you are trying to compare two 4-bit 2's complement numbers, create a table with the A-numbers horizontally (-8 to +7) and the B-numbers vertically (-8 to +7). Now fill in the interior of the table with the result of the comparison you want (e. g. A>B). After you have done that, start thinking about how to implement it.