Digital Comparator Calculator

This tool computes the three fundamental magnitude comparison outputs: A > B, A = B, and A < B for two unsigned binary numbers represented within a specified bit width. It performs signed or unsigned comparison logic based on user input (defaulting to unsigned), and displays the Boolean result for each condition.

Engineers use it to verify comparator logic before implementing hardware—such as 74LS85 ICs or FPGA-based comparators—and to validate ALU behavior, sorting algorithms, priority encoders, or control-state transitions where magnitude decisions drive system flow.

Bit Width defines the number of bits used to represent each number (e.g., 4-bit, 8-bit, 16-bit). It determines the maximum representable value (2^w−1 for unsigned) and affects overflow handling—exceeding this width truncates or wraps values, potentially altering comparison results.

Yes—when interpreting inputs as signed (two’s complement), the calculator adjusts the comparison logic accordingly. For example, with 8-bit width, inputting A = 255 is interpreted as −1, and A = B will reflect signed equality. Ensure bit width matches your number’s signed representation.

Common widths include 4-bit (nibbles, simple controllers), 8-bit (legacy microcontrollers, ADC outputs), 16-bit (audio processing, embedded systems), and 32/64-bit (modern CPUs, high-precision DSP). Choose width based on your system’s data path and required dynamic range.

Large inputs may exceed the selected bit width’s representable range, causing silent wraparound (e.g., 256 in 8-bit becomes 0). Always verify that both A and B fall within [0, 2^w−1] for unsigned or [−2^w−1, 2^w−1−1] for signed interpretation.

It performs arithmetic equality: A = B evaluates to true only when the numeric values are identical, regardless of bit-level representation. This differs from bitwise XOR-equality checks—it reflects functional equivalence in magnitude comparison logic.

While it doesn’t synthesize full gate diagrams, the output directly maps to standard comparator building blocks: A=B uses XNOR chains and AND reduction; A>B uses MSB-first cascaded comparisons. These outputs feed into larger combinational logic or HDL (e.g., Verilog assign statements).

Not natively—the current interface supports single-pair evaluation. For repeated comparisons, engineers typically export inputs to scripts (Python, MATLAB) or integrate the underlying logic into testbenches or spreadsheet models using the same magnitude comparison algorithm.

This calculator emulates the core functionality of these TTL/CMOS magnitude comparators—producing identical A>B, A=B, A