Binary Arithmetic and Bitwise Logic
Binary calculators serve two genuinely different purposes: arithmetic (ADD, SUB) treats the binary strings as base-2 numbers, carrying and borrowing across bit positions exactly like decimal addition does across digit positions. Bitwise operations (AND, OR, XOR) instead treat each bit position independently, comparing the two inputs bit-by-bit with no carrying at all — a fundamentally different operation from arithmetic, despite superficially looking similar on binary strings.
This distinction trips up a lot of people learning digital logic for the first time: 1010 AND 0110 compares each column independently (producing 0010), while 1010 + 0110 carries between columns (producing 10000) — same two inputs, very different results depending on which operation you actually mean.
Binary arithmetic and bitwise logic underpin everything from CPU instruction execution to network subnet masking (see the CIDR calculator for a real-world bitwise AND application), which is why being able to verify both by hand against a known-correct tool matters for coursework and debugging alike.