Experiment 2 - The 2-bit Identity Comparator

How can vou verify if two 2-bit numbers are the same? For this you need more than just XNOR gates.

An identity comparator compares two 2-bit numbers by checking each digit individually using a XNOR gate. From the truth table you can see that this is not enough. Only if x₀ is identical with y₀ AND x₁ is identical with y₁, are the two numbers identical. You need an extra AND gate.

x1 x0 y1 y0 x=y 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 Truth table of a 2-bit identity comparator.

Circuit diagram of a 2-bit identity comparator. Circuit of a 2-bit identity comparator. (Enlarge)

This concept can be extended to arbitrarily large numbers...