Binary Multiplication Calculator — Multiply Binary Numbers
Enter two binary numbers to multiply them. The calculator uses the shift-and-add (long multiplication) method and shows each partial product so you can follow the working.
Binary: 11110 • Hex: 0x1E
Bit at position 1 is 1 → A × 2^1 = A << 1
Bit at position 0 is 1 → A × 2^0 = A << 0
Sum of all partial products
- 1
A in decimal
10 - 2
B in decimal
3 - 3
Product A × B
10 × 3 = 30Computed via shift-and-add: each 1-bit in B contributes a shifted copy of A.
How does this calculator work?
Binary multiplication uses shift-and-add: for each 1-bit in B at position i, shift A left by i to get a partial product, then sum all partial products. A × 0011₂ is simply A shifted left once (×2) plus A shifted left zero times (×1). Enter two binary numbers above to see the partial products and the result in binary, decimal, and hex.
Formula
How this is calculated
Binary multiplication mirrors long multiplication in decimal but is simpler because each bit of the multiplier is either 0 or 1. For every 1-bit in B (starting from the most significant end), the algorithm shifts A left by the bit's position index (equivalent to multiplying by the corresponding power of 2) to form a partial product. For every 0-bit, the partial product is zero and is skipped. The final product is the sum of all non-zero partial products.
This is the shift-and-add algorithm: shift A left by i positions if the i-th bit of B is 1, then add those shifted values. Hardware multipliers optimise this using carry-save adders and Wallace trees, but the underlying operation is identical.
This calculator uses arbitrary-precision JavaScript BigInt arithmetic, so the product is always exact regardless of the size of the operands. Up to 16 partial products are shown in the step trace; larger operands still compute the correct product but the step list is truncated.
Frequently asked questions
Multiplying two n-bit numbers can produce a result up to 2n bits wide. For example, 1111₂ (15) × 1111₂ (15) = 11100001₂ (225), which takes 8 bits to represent even though each operand is only 4 bits.
A partial product is the result of multiplying A by a single bit of B at a given position. If the bit is 1, the partial product is A shifted left by the bit's position (A × 2^i). If the bit is 0, the partial product is 0. Summing all partial products gives A × B.
Modern CPUs use parallel multiplier circuits (Wallace trees or Booth encoders) to compute many partial products simultaneously and reduce them in a tree of adders. The logical result is identical to shift-and-add but far faster.
Also known as
TG we-Calculate Editorial Team. (2026). Binary Multiplication Calculator — Multiply Binary Numbers [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/binary-multiplication-calculator
TG we-Calculate Editorial Team. "Binary Multiplication Calculator — Multiply Binary Numbers." TG we-Calculate. 2026. https://we-calculate.com/calculator/binary-multiplication-calculator.
TG we-Calculate Editorial Team, "Binary Multiplication Calculator — Multiply Binary Numbers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/binary-multiplication-calculator
@misc{wecalculate_binary_multiplication_calculator, title = {Binary Multiplication Calculator — Multiply Binary Numbers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/binary-multiplication-calculator}}, year = {2026}, note = {TG we-Calculate} }
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