Magnitude Comparator
Tells whether A < B, A = B, or A > B for two binary numbers.
Description
A circuit that orders two numbers (less, equal, greater). Decisions, sorting, and bounds checks all need comparison. XNOR each bit for equality; scan from MSB to find the first difference.
- A = B when every bit pair is equal (all XNORs are 1).
- Otherwise the highest differing bit decides: a 1 in A there means A > B.
- What: A circuit that orders two numbers (less, equal, greater).
- Why: Decisions, sorting, and bounds checks all need comparison.
- How: XNOR each bit for equality; scan from MSB to find the first difference.
- Where: ALUs (condition flags), address-range logic, sort hardware.
- When: Any branch or selection based on numeric order.
- A>B = A·B′
- A<B = A′·B
- A=B = A⊙B (XNOR)
At a glance
What
A circuit that orders two numbers (less, equal, greater).
Why
Decisions, sorting, and bounds checks all need comparison.
How
XNOR each bit for equality; scan from MSB to find the first difference.
Where
ALUs (condition flags), address-range logic, sort hardware.
When
Any branch or selection based on numeric order.
Think of it like…
Like comparing two phone numbers digit by digit from the left: the first place they differ decides which is bigger — earlier digits outrank later ones.
How it decides
- A = B when every bit pair is equal (all XNORs are 1).
- Otherwise the highest differing bit decides: a 1 in A there means A > B.
Outputs
| Condition | Asserted output |
|---|---|
| all bits equal | A = B |
| first diff: A bit = 1 | A > B |
| first diff: A bit = 0 | A < B |
Black-box view
Inputs on the left → outputs on the right · particles show signal direction
Logic diagram
Click inputs to toggle · glowing wires carry 1 · particles show signal direction
The 5 Whys
- 1
Why a comparator? Programs constantly test order and equality.
- 2
Why scan from the MSB? The most-significant differing bit dominates magnitude.
- 3
Why XNOR for equality? XNOR is 1 exactly when two bits match.
- 4
Why dedicated hardware? Comparison is on the critical path of branches.
- 5
Root cause: ordering reduces to equality plus first-difference detection.
Cheat sheet
Working principle
- XNOR each bit for equality; scan from MSB to find the first difference.
- A circuit that orders two numbers (less, equal, greater).
Formulas & Boolean expressions
- A>B = A·B′
- A<B = A′·B
- A=B = A⊙B (XNOR)
- A = B when every bit pair is equal (all XNORs are 1).
- all bits equal = A = B
- first diff: A bit = 1 = A > B
- first diff: A bit = 0 = A < B
Key facts
- A = B when every bit pair is equal (all XNORs are 1).
Why it exists
- Root cause: ordering reduces to equality plus first-difference detection.