Binary multiplication forms shifted partial products and adds them. An array multiplier arranges AND gates and adders into a regular structure. Signed multiplication must account for sign extension or use a signed algorithm, such as Booth recoding, rather than blindly treating every bit as positive.
Worked example
Unsigned 101 × 011 means 5 × 3. The multiplier bits produce partial products 00101 and 01010; the third partial product is zero. Their sum is 01111, or 15. A full product of two n-bit operands can require 2n bits.
What to watch for
For signed operands, the most significant bit has negative weight in twos complement. Unsigned partial-product interpretation would give the wrong answer for a negative operand.
Try it yourself
What full-width binary product comes from three-bit unsigned 111 × 010?
Answer: 7 × 2 = 14, which is 001110 in six bits.
How to study this topic
State the operand width and signedness first. Work out a decimal answer, then compare it with the binary result. Keep result bits, carry, borrow and signed overflow distinct when interpreting the circuit's output.
Explore related programmes
These recorded programmes are upcoming. This article is general educational content, not a syllabus or course sample.
Digital Electronics