Binary Multiplier
Multiplies by ANDing bits to form partial products, then adding them.
Description
A circuit that multiplies two binary numbers. Multiplication is fundamental to DSP, graphics, and addressing. Form partial products with AND gates, shift them, and sum with adders.
- Each bit of the multiplier ANDs the whole multiplicand → one partial product.
- Partial products are shifted by their bit position.
- An adder tree (or array) sums them into the final product.
- What: A circuit that multiplies two binary numbers.
- Why: Multiplication is fundamental to DSP, graphics, and addressing.
- How: Form partial products with AND gates, shift them, and sum with adders.
- Where: ALUs, DSP MAC units, GPU shader cores.
- When: Any time products are computed in hardware.
- Analogy — Just like long multiplication on paper: write a shifted copy of the top number for each bottom digit, then add the stack. In binary each 'copy' is simply the number or nothing (AND).
At a glance
What
A circuit that multiplies two binary numbers.
Why
Multiplication is fundamental to DSP, graphics, and addressing.
How
Form partial products with AND gates, shift them, and sum with adders.
Where
ALUs, DSP MAC units, GPU shader cores.
When
Any time products are computed in hardware.
Think of it like…
Just like long multiplication on paper: write a shifted copy of the top number for each bottom digit, then add the stack. In binary each 'copy' is simply the number or nothing (AND).
Partial products
- Each bit of the multiplier ANDs the whole multiplicand → one partial product.
- Partial products are shifted by their bit position.
- An adder tree (or array) sums them into the final product.
2×2 multiply example (10 × 11 = 0110)
| Value | |
|---|---|
| Multiplicand | 10 (2) |
| Multiplier | 11 (3) |
| PP0 (×1) | 10 |
| PP1 (×1, shift) | 100 |
| Product | 0110 (6) |
Black-box view
Inputs on the left → outputs on the right · particles show signal direction
Functional / block diagram
Functional blocks · arrows animate in the direction data flows
The 5 Whys
- 1
Why partial products? Binary multiply is shift-and-add of ANDed rows.
- 2
Why AND for each bit? A bit times a number is the number or zero.
- 3
Why shift? Each multiplier bit has a positional weight.
- 4
Why an adder tree? To sum many partial products quickly.
- 5
Root cause: multiplication reduces to parallel AND + structured addition.
Cheat sheet
Working principle
- Form partial products with AND gates, shift them, and sum with adders.
- A circuit that multiplies two binary numbers.
Formulas & Boolean expressions
- Multiplicand = 10 (2)
- Multiplier = 11 (3)
- PP0 (×1) = 10
- PP1 (×1, shift) = 100
- Product = 0110 (6)
Key facts
- Each bit of the multiplier ANDs the whole multiplicand → one partial product.
Why it exists
- Root cause: multiplication reduces to parallel AND + structured addition.