How this instrument works
Multiplying two binary numbers follows the identical rules as decimal multiplication — it's just the place values underneath (ones, twos, fours, eights) that differ. This page keeps both inputs restricted to 0 through 3 (representable in just 2 bits each) so that even their largest possible product, 9, still fits comfortably within the 4-bit range this site's other binary pages use, with no overflow or wraparound to complicate the result.
That restriction matters because multiplication grows results much faster than addition or subtraction does — two 4-bit numbers (up to 15 each) could multiply to as high as 225, far beyond what 4 bits alone could hold. Scoping the inputs down to 2 bits each keeps the entire calculation, start to finish, inside the same 4-bit frame this site's other binary pages already use.
The product itself is computed in ordinary arithmetic, then converted into its own binary digits the same way this site's Binary Calculator converts any whole number — repeatedly dividing by 2 and tracking the remainder at each place.
- Enter the first number (0 to 3) into the First number field.
- Enter the second number (0 to 3) into the Second number field.
- Read the four Product bit fields — the result's own binary digits.
- Multiply each bit by its place value (8, 4, 2, 1) and add them together to confirm the total matches the expected decimal product.
Worked example — 3 times 3
3 (11) times 3 (11) is 9 in decimal, which converts to 1001 in binary. Checked in reverse: 1×8+0×4+0×2+1×1=9, confirming the product's own bit pattern.
2 (10) times 2 (10) is 4 (0100). 0 (00) times 3 (11) is 0 (0000) — multiplying by zero clears every bit, in binary exactly as it does in decimal, regardless of what the other number happens to be.
Questions
Why are the inputs restricted to just 0 through 3?
Multiplication grows results far faster than addition does — two full 4-bit numbers could multiply to as high as 225, well beyond 4 bits' own capacity — so restricting both inputs to 2 bits each keeps every possible product safely within the 4-bit range this site's other binary pages already use.
What is the largest product this calculator can compute?
9, from multiplying the two largest 2-bit inputs, 3 and 3 — which converts to 1001 in binary, still comfortably within 4 bits.
Does binary multiplication ever need to worry about overflow the way binary addition does?
It can, if the inputs are large enough relative to the output width available — this page sidesteps that entirely by restricting the inputs small enough that overflow simply can't happen.
How is this different from the Binary Calculator page on this site?
That page converts any single whole number into binary; this page multiplies two numbers together first and then converts THAT product into its own binary digits.
What happens when one of the numbers is 0?
The product is always 0 (0000), regardless of the other number — multiplying by zero clears every bit, exactly as it clears every decimal digit in ordinary base-10 arithmetic.