Building Blocks and Equality Comparators

Start here Nobody builds a house one grain of sand at a time. Builders use bricks, doors and windows: ready-made parts. Circuit designers work the same way. Instead of placing every gate by hand, they use ready-made building blocks like comparators, decoders and multiplexers. This week you meet the most common ones.

A combinational building block is a group of gates that does one common job. It usually has tens to hundreds of transistors. (This size was once called MSI: Medium Scale Integration.)

Why use them? They hide the gate-level details. You only need to know what the block does, not how every gate inside is wired.

Question: are bits x and y the same?

• XOR gives 1 when the bits are different.
• XNOR $\left(\operatorname{XOR} + \operatorname{NOT}\right)$ gives 1 when the bits are equal.

So a 1-bit equality comparator is just an XNOR gate.

Two numbers are equal only if every pair of matching bits is equal.

1. Put one XNOR on each bit pair ($A_{0}$ with $B_{0} , A_{1}$ with $B_{1} , \ldots$).
2. AND all the XNOR outputs together.

Lecture example — 11 vs 9 $A = 1 1 =$ 1011, $B = 9 =$ 1001

Bit	3	2	1	0
A	1	0	1	1
B	1	0	0	1
XNOR	1	1	0	1

One XNOR gives 0 (bit 1 differs), so the AND gives 0 → A ≠ B.

Everyday example: checking a 4-digit door lock code. The lock opens only if every digit matches. One wrong digit and it stays shut. That’s the AND of all the “digit matches” checks.

In one line: Building blocks are ready-made gate groups. An equality comparator is one XNOR per bit, all ANDed together. Exam words: combinational building block, MSI, comparator, equality comparator, XNOR, N-bit comparison.