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Binary to Decimal

Convert binary (any length) to decimal with a per-bit place-value table showing 2^n contribution for each set bit. 32/64-bit inputs are also decoded as IEEE 754 floats. BigInt-backed for arbitrary precision. 100% offline.

What is the Binary to Decimal?

Binary to Decimal is a focused single-direction converter built around the binary number system's underlying maths. Type any binary input (with or without `0b` prefix, optionally negative, underscores / commas / spaces ignored) and the tool produces: the canonical decimal value (BigInt, arbitrary precision), a per-bit place-value table from MSB to LSB showing which 2^n term each bit contributes, and a sum-of-set-bits breakdown like `2^7 + 2^6 + 2^0 = 128 + 64 + 1 = 193`. When the input is exactly 32 or 64 bits we additionally decode it as an IEEE 754 single- or double-precision float — showing the sign bit, biased and effective exponent, mantissa, computed value, and classification (zero / subnormal / normal / infinity / NaN). Useful for both learning binary fundamentals and debugging the binary representation of floats in low-level code.

How to use it

  1. Type a binary number — with or without `0b` prefix, optional minus sign.
  2. Read the decimal value at the top.
  3. Scan the place-value table to see how each bit contributes (highlighted rows = set bits).
  4. When the input is exactly 32 or 64 bits, read the IEEE 754 single/double-precision interpretation.

Benefits

  • BigInt-backed — arbitrary precision, no rounding errors for 64+ bit inputs.
  • Per-bit place-value table showing 2^n contribution for every position.
  • Sum-of-set-bits breakdown for educational use.
  • IEEE 754 float decoder for 32-bit and 64-bit inputs (single + double precision).
  • Float classification: zero / subnormal / normal / infinity / NaN.
  • Accepts `0b` prefix, underscores, commas and spaces — paste with whatever formatting.
  • Negative numbers via leading minus sign (signed magnitude).
  • Runs 100% in your browser — Toollyz has no server.

Frequently asked questions

How is this different from the Hexadecimal Converter?

The Hexadecimal Converter shows all four bases (2/8/10/16) side-by-side. This tool is a focused binary-to-decimal view with two extras: the place-value table breaking down each bit's contribution, and the IEEE 754 float decoder for 32/64-bit inputs.

What's a place-value table?

A row per bit from MSB to LSB. Each row shows the position (2^n exponent), the bit value (0 or 1), and the contribution to the total (2^n if the bit is set, 0 if not). Sum the contributions and you get the decimal value.

What's IEEE 754?

The standard for representing floating-point numbers in binary. Single precision (32 bits) = 1 sign + 8 exponent + 23 mantissa bits. Double precision (64 bits) = 1 sign + 11 exponent + 52 mantissa bits. Almost all CPUs and programming languages use this format.

Why decode 32 and 64 bit specifically?

Those are the IEEE 754 single and double precision widths. Half-precision (16-bit) and extended-precision (80/128-bit) exist but are less common. Half precision support may be added later.

What's a subnormal float?

When the exponent is 0 but the mantissa isn't, the number is 'subnormal' (or denormal) — it has reduced precision but extends the float range closer to zero. Common in graphics and physics simulations near zero.

Can I handle 128-bit binary?

Yes for integer mode — BigInt has no fixed maximum. The IEEE 754 decoder caps at 64 bits because that's what the spec defines for double precision.

How does negative binary work?

We use signed-magnitude (leading minus sign). `-1010` is decimal -10. Two's complement is NOT supported because there's no obvious bit width to assume — for two's complement, specify the width and use a specialised tool.

What about floating-point binary literals like `1.01`?

Not supported in this tool. Fixed-point binary fractions would need a different parser; for now, the IEEE 754 mode covers floating-point use cases.

Will set/zero bits be counted accurately for huge numbers?

Yes — BigInt bit manipulation is exact. For a 1024-bit number you'll see 1024 rows in the place-value table.

Why are the position numbers different from the bit indices?

We use the standard convention: position N corresponds to the bit weighted 2^N. The MSB has the highest position; the LSB has position 0. Bit indices match positions in this tool.

Is anything uploaded?

No. Parsing and conversion are pure browser computations.

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