The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London.

For each bit y i, for i running from 0 to N 1, the bits y i and y i 1 are considered.

Where these two bits are equal, the product accumulator P is left unchanged.

Where y i 0 and y i 1 1, the multiplicand times 2 i is added to P; and where y i 1 and y i1 0, the multiplicand times 2 i is subtracted from P.

Typically, it proceeds from LSB to MSB, starting at i 0; the multiplication by 2 i is then typically replaced by incremental shifting of the P accumulator to the right between steps; low bits can be shifted out, and subsequent additions and subtractions can then be done just on the highest N bits of P.

There are many variations and optimizations on these details.

When a string runs through the MSB, there is no high-order 1, and the net effect is interpretation as a negative of the appropriate value.

Each turn of the crank handle adds (up) or subtracts (down) the operand set to the top register from the value in the accumulator register at the bottom.

Shifting the adder left or right multiplies the effect by ten.

Let m and r be the multiplicand and multiplier, respectively; and let x and y represent the number of bits in m and r.

One possible correction to this problem is to add one more bit to the left of A, S and P.

This then follows the implementation described above, with modifications in determining the bits of A and S; e.g., the value of m, originally assigned to the first x bits of A, will be assigned to the first x 1 bits of A.

Below, the improved technique is demonstrated by multiplying 8 by 2 using 4 bits for the multiplicand and the multiplier.

The number of operations can be reduced to two by rewriting the same as.

When the ones in a multiplier are grouped into long blocks, Booths algorithm performs fewer additions and subtractions than the normal multiplication algorithm.

IV (2): 236240. Archived (PDF) from the original on 2018-07-16.

Signal processing handbook.

CRC Press. p. 234.

ISBN 978-0-8247-7956-6.

Computer Organization and Design: The HardwareSoftware Interface (Second ed.).

San Francisco, California, USA: Morgan Kaufmann Publishers.

Computer Organization and Architecture: Designing for performance (Fifth ed.).

New Jersey: Prentice-Hall, Inc.

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Booths Algorithm C Program