# Help with Boolean circuit design

Discussion in 'Homework Help' started by Estudent1005, Jan 5, 2011.

1. ### Estudent1005 Thread Starter New Member

Jan 5, 2011
4
0
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.

2. ### n1ist Senior Member

Mar 8, 2009
176
17
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

3. ### Estudent1005 Thread Starter New Member

Jan 5, 2011
4
0
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!

Last edited: Jan 6, 2011
4. ### Estudent1005 Thread Starter New Member

Jan 5, 2011
4
0
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

5. ### Georacer Moderator

Nov 25, 2009
5,178
1,286
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.