I'm stuck on this homework question and was hoping for some help:

Design a Boolean circuit that compares whether two-bit unsigned numbers are equal.

I was given the hint : Construct a truth table and use XOR, AND, and NOT gates.

Any advice on this one?

 

Well, you have 4 inputs and one output. Start by drawing the truth table (what does it mean when two two-bit unsigned numbers are equal?) Then figure out the logic from that.

/mike

 

I understand the input logic (i think)

would the inputs to the truth table look similiar to this:

X1 X2 Y1 Y2
0 0 0 0
0 1 0 1
1 0 1 0
1 1 1 1


how do I begin to create the Boolean function? From there, I know how to calculate the output and how to build the circuit, just stuck on the formula part..

Thanks again!

 

do I need to show 2 formulas that are equal?
for example:

x1 XOR x2 = y1 NOTy2 AND NOTy1 y2

something like that?

x1, x2, y1, y2 being my input variables

 

The XOR gate has the property of giving a 1 if its two inputs are different. Therefore, if you pass the 4 bits through 2 XORs, and see even one 1, your numbers are different. I don't think a truth table will be of much help here. Just use your logic to sort this out.