Binary Comparator Calculator
Compare two unsigned binary numbers and instantly determine whether A is greater than, equal to or less than B. See decimal equivalents, magnitude difference, normalized values, comparison width and the first differing binary position.
What Is a Binary Comparator Calculator?
A Binary Comparator Calculator compares two binary numbers and determines their relative magnitude. For two values A and B, the result can be A greater than B, A equal to B, or A less than B.
Unlike binary addition or subtraction, a magnitude comparator is mainly designed to produce a logical relationship result. Comparator circuits are widely used in digital electronics, processors, control systems, sorting logic and address matching.
This calculator treats both inputs as unsigned binary integers and also shows decimal values, normalized bit patterns, the absolute magnitude difference and the first bit where the two numbers differ.
Binary Magnitude Comparator Outputs
A Greater Than B
The greater-than output becomes active when A represents a larger unsigned binary value than B.
GT = 1
A Equal To B
The equality output becomes active when both binary numbers represent exactly the same numerical value.
EQ = 1
A Less Than B
The less-than output becomes active when A represents a smaller unsigned binary value than B.
LT = 1
Comparator Flags
For a valid binary comparison, one of GT, EQ or LT identifies the relationship between A and B.
1-Bit Binary Comparator Truth Table
| A | B | A > B | A = B | A < B |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 |
1-Bit Comparator Boolean Equations
Greater Than
Less Than
Equal
XNOR Equality
XNOR is commonly used for individual-bit equality because it produces 1 when both inputs have the same state.
How Multi-Bit Binary Comparison Works
For unsigned binary values, comparison begins at the most significant position. If both bits are equal, the comparison continues toward the less significant positions.
The first high-order position where A and B differ determines which binary value is larger.
B = 100111
Compare from the left:
1 = 1
0 = 0
1 > 0
Therefore:
A > B
Worked Example: A Greater Than B
B = 1001
1011 binary = 11 decimal
1001 binary = 9 decimal
11 > 9
GT = 1
EQ = 0
LT = 0
Worked Example: Equal Binary Numbers
B = 110101
All corresponding bits match.
A = B
GT = 0
EQ = 1
LT = 0
Worked Example: A Less Than B
B = 1010
0110 binary = 6 decimal
1010 binary = 10 decimal
6 < 10
GT = 0
EQ = 0
LT = 1
Leading Zeros in Binary Comparison
Leading zeros do not change the value of an unsigned binary integer. Binary 101 and binary 00101 both represent decimal 5.
B = 101
Normalized A = 00101
Normalized B = 00101
A = B
Binary Comparison Examples
| A | B | A Decimal | B Decimal | Result |
|---|---|---|---|---|
| 0000 | 0000 | 0 | 0 | A = B |
| 0001 | 0000 | 1 | 0 | A > B |
| 0011 | 0100 | 3 | 4 | A < B |
| 0111 | 0111 | 7 | 7 | A = B |
| 1000 | 0111 | 8 | 7 | A > B |
| 1010 | 1100 | 10 | 12 | A < B |
| 1111 | 1110 | 15 | 14 | A > B |
Binary Comparator vs Binary Subtraction
| Feature | Binary Comparator | Binary Subtraction |
|---|---|---|
| Main purpose | Determine relationship | Calculate difference |
| Typical output | GT, EQ, LT | Difference bits |
| Borrow calculation | Not required | May be required |
| Equality | Direct result | Can be inferred from zero |
| Typical use | Decision logic | Arithmetic logic |
Where Binary Comparators Are Used
Digital Logic
Comparator circuits generate logical outputs based on the relationship between two binary quantities.
Processor Decisions
Comparison operations support conditional decisions, branches and numerical evaluation inside processors.
Address Matching
Digital systems can compare binary addresses, register values and identifiers.
Sorting and Selection
Comparator circuits can help select larger or smaller values in digital sorting and selection systems.
Important Binary Comparator Notes
Leading zeros do not alter the numerical value.
When inputs have different lengths, the shorter value is padded with leading zeros before bit-by-bit analysis.
For unsigned numbers, the first differing high-order bit determines the larger value.
Signed two’s-complement values require different comparison rules because the most significant bit also represents the sign.