AnyTool
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How do I use an online binary calculator?

Type Value A and Value B in binary (or switch the input base to decimal, octal or hex), pick a word size (8, 16, 32 or 64 bits), then choose an operation — add, subtract, multiply, divide, modulo, AND, OR, XOR, NOT, left shift, right shift or negate. AnyTool Binary Calculator computes the answer live with BigInt for exact digits and shows the result in binary first, grouped into nibbles, with decimal (signed and unsigned), hex and octal alongside. A bit-by-bit carry trace explains how a binary add or subtract works, a two’s-complement panel shows invert-then-add-1, and a clickable bit grid lets you flip individual bits. It is a programmer (integer) calculator, so values wrap at the chosen width like a CPU register, and nothing you type leaves your browser.

  • Enter operands in binary (default), or decimal, octal and hex — switch any time
  • Arithmetic (+ − × ÷ mod) and bitwise (AND, OR, XOR, NOT, shifts) plus negate
  • Result shown in binary first (nibble-grouped), then decimal, hex and octal
  • Step-by-step carry/borrow trace and a two’s-complement (invert + 1) view
  • 100% in your browser — exact BigInt math, no upload, no signup, works offline

What is

Binary calculator

A binary calculator performs integer arithmetic and bitwise logic on numbers expressed in base 2, showing the result as a binary bit pattern (and usually in decimal, hex and octal too). Beyond binary add, subtract, multiply, divide and modulo it offers AND, OR, XOR, NOT and bit shifts, and it interprets values at a fixed word size (8, 16, 32 or 64 bits) using two’s complement, so negatives and overflow wrap like a hardware register. AnyTool implements one entirely in the browser with a reusable BigInt engine, so every bit is exact at any width, and it adds a bit-by-bit carry trace to teach how binary arithmetic actually works.

Calculators

Related terms

Two’s complementBitwise operationBinary additionWord sizeBit shift

Frequently Asked Questions

You add column by column from the right: 0+0 is 0, 1+0 is 1, and 1+1 is 0 with a carry of 1 into the next column. The calculator shows each carry step.

Binary addition works just like decimal but in base 2, so the only "carry" rule is that 1 plus 1 equals 0 with a 1 carried to the next more-significant column, and 1 plus 1 plus an incoming carry equals 1 with a carry. AnyTool Binary Calculator displays a bit-by-bit trace that lines up Value A, Value B and the carry row above the result so you can see exactly where each carry comes from, and if the final carry leaves the most-significant bit it overflows the chosen word size and is discarded.

It uses two’s complement at the chosen word size: subtraction borrows column by column, and a value below zero is stored as its two’s-complement bit pattern (invert the bits and add 1).

Negative binary values are represented in two’s complement at a fixed word size, which is the value plus 2 to the power of the word size — so −1 in an 8-bit word is 11111111. AnyTool Binary Calculator subtracts using the schoolbook borrow method and shows each borrow in the trace; when A is smaller than B the result is the negative two’s-complement pattern. A dedicated panel demonstrates the negation itself by inverting every bit of the result and adding 1, and the signed decimal reading is shown beside the unsigned one.

A logical right shift fills the vacated high bits with zeros; an arithmetic shift copies the sign bit. This tool performs a logical (unsigned) right shift.

Shifting a binary number right by n moves every bit n places toward the least-significant end. A logical right shift always brings in zeros at the top, treating the value as unsigned, while an arithmetic right shift replicates the sign bit so negative numbers stay negative. AnyTool Binary Calculator performs a logical right shift on the raw bit pattern at the selected word size, and a left shift fills the low bits with zeros (multiplying by powers of two until bits fall off the top of the word).

It is a programmer calculator built for integers and bit patterns, so division truncates toward zero and there is no binary point — 7 ÷ 2 is 3.

Programmer calculators model how a CPU works with registers and bits, where values are whole numbers of a fixed width. AnyTool Binary Calculator follows that model: division and modulo truncate toward zero like C integer math, so 111 ÷ 10 (7 ÷ 2) returns 11 (3) with no fractional binary point, and bitwise operations act on exact bit patterns. For real-number arithmetic with decimals, roots or trigonometry, use the Scientific Calculator instead.

Detailed Explanation

Methodology

How the Binary Calculator Computes Each Operation

AnyTool Binary Calculator runs a pure, unit-tested programmer engine entirely in the browser, with binary as the default base. Each operand — typed in binary, decimal, octal or hexadecimal — is parsed into a single canonical BigInt, so every bit is exact even for 64-bit values that would round under JavaScript’s 53-bit doubles. The value is then masked to the chosen word size to produce the unsigned bit pattern a register would hold. Arithmetic (add, subtract, multiply, integer divide and modulo) is performed on the signed two’s-complement interpretation and truncates toward zero like C; bitwise AND, OR, XOR and NOT act on the raw patterns; left and right shifts are logical shifts on the masked value. Every result is wrapped back to the word width and presented in binary first, and the same base-agnostic engine powers the Hex Calculator.

  • Operands parsed to exact BigInt, then masked to the word size
  • Arithmetic uses signed two’s complement; division truncates toward zero
  • Bitwise AND/OR/XOR/NOT on raw patterns; logical left/right shifts
  • Results wrapped to 8/16/32/64 bits like a hardware register
  • Same base-agnostic engine as the Hex Calculator, binary-first UI
How It Works

Carry Traces, Two’s Complement and the Bit Grid

Beyond computing answers, the Binary Calculator teaches how binary arithmetic works. A bit-by-bit trace lines up Value A, Value B and a carry (or borrow) row above the result, so you can follow exactly how 1 + 1 carries to the next column or how subtraction borrows when A is smaller than B. A separate two’s-complement panel demonstrates negation by inverting every bit of the result and adding 1, with the signed decimal shown beside the unsigned one. Results appear in binary first, grouped into nibbles for readability, then in decimal (signed and unsigned), hex and octal, each one tap to copy, and a clickable bit grid grouped into bytes lets you flip individual bits of Value A and watch every base update live.

  • Step-by-step carry trace for binary addition
  • Step-by-step borrow trace for binary subtraction
  • Two’s-complement panel shows invert-then-add-1 negation
  • Binary-first result, nibble-grouped, plus decimal/hex/octal
  • Clickable, byte-grouped bit grid flips individual bits live
Limitations

Integer-Only Math and Word Wrapping

This is a binary programmer calculator, so it works only with whole numbers. Division and modulo truncate toward zero (7 ÷ 2 = 3) with no binary point, and there are no roots, logarithms or trigonometry. Because results are masked to the chosen word size, any value that exceeds the range overflows and wraps around rather than growing, exactly as it would in a fixed-width CPU register — the tool surfaces the exact pre-wrap value when this happens so the behaviour is never silent. Bitwise NOT, shifts and negate depend entirely on the word size you select, since they operate on a specific number of bits: a NOT at 8-bit differs from a NOT at 32-bit. AnyTool states this plainly: for real-number arithmetic with decimals, use the Scientific Calculator instead.

  • Whole numbers only — division truncates toward zero (7 ÷ 2 = 3)
  • Results wrap at the word size like a hardware register
  • Overflow is shown explicitly with the exact pre-wrap value
  • NOT, shifts and negate depend on the chosen 8/16/32/64-bit width
  • For decimals, roots and trig use the Scientific Calculator
Binary math: in-browser (AnyTool) vs typical online binary calculators
CapabilityAnyToolTypical online calculators
Where it runs100% in your browserOften server-side
PrecisionExact BigInt at any widthOften JS doubles (rounds past 2⁵³)
PresentationBinary first, then dec/hex/octOften binary only or pairs
Bitwise opsAND, OR, XOR, NOT, shiftsSometimes a subset
Word size8/16/32/64-bit, selectableOften fixed or unstated
Carry/borrow traceStep-by-step, visualRarely shown
Two’s complementSigned view + invert/+1 panelOften unsigned only
Bit gridClickable, byte-groupedRarely interactive
Works offlineYes (PWA)No
Cost / signupFree, no signupOften ad-heavy or gated

AnyTool computes every operation locally with an exact, unit-tested BigInt engine and uploads nothing.