Multiply binary numbers using the shift-and-add algorithm. Shows partial products and final result.
2026-03-28T00:00:00Z
Binary multiplication is the process of multiplying two numbers in base-2 format. Like decimal multiplication, it follows the same principles but is simpler because you only work with 0s and 1s. The basic rules are: 0×0=0, 0×1=0, 1×0=0, and 1×1=1.
The standard algorithm for binary multiplication is called "shift and add." For each bit in the multiplier: if it's 1, write down the multiplicand shifted left by the bit's position; if it's 0, skip it. Finally, add all the shifted values together using binary addition. This method mirrors how multiplication works in hardware at the transistor level.
Binary multiplication is fundamental to computer processors. Modern CPUs implement optimized multiplication algorithms like Booth's algorithm or Wallace tree multipliers for speed. Understanding binary multiplication helps in low-level programming, digital design, cryptography, and anywhere precise control over mathematical operations is needed.
101 (5 in decimal)
× 11 (3 in decimal)
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101 (1 × 101, shifted 0)
101 (1 × 101, shifted 1)
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1111 (15 in decimal)Note: The calculator shows partial products and the final result. For a complete step-by-step binary addition breakdown of the partial products, refer to the binary addition calculator.
Multiply 1010₂ (10) by 110₂ (6):
10100 + 101000 -------- 111100 (60 in decimal)
Binary multiplication tables only have four rules (0×0, 0×1, 1×0, 1×1), all resulting in either 0 or 1. Decimal requires memorizing 100 multiplication facts (0×0 through 9×9).
CPUs use hardware multipliers with optimized circuits. Simple processors use shift-and-add; advanced processors use parallel algorithms like Booth's algorithm or Wallace trees for speed.
No! Multiplication requires multiple shifts and additions, making it slower than a single addition. Modern CPUs take 3-5 cycles for multiplication vs 1 cycle for addition.
Yes! Use two's complement representation for negative numbers, multiply as normal, then interpret the result in two's complement. Or use signed multiplication algorithms built into CPUs.
For very large numbers, algorithms like Karatsuba multiplication or FFT-based multiplication are faster than the shift-and-add method, reducing computational complexity.
Everywhere in computing: graphics rendering, cryptography, hash functions, compression algorithms, digital signal processing, scientific simulations, and any mathematical computation.
Booth's algorithm reduces the number of additions by encoding the multiplier into signed digits (-1, 0, 1), replacing long sequences of 1s with a subtraction and addition.
It depends on your system. 32-bit integers can multiply numbers up to 2³²-1; 64-bit systems handle up to 2⁶⁴-1. For larger numbers, use arbitrary-precision libraries.
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