How this instrument works
Dividing one whole number by another produces two results: a quotient (how many whole times the divisor fits) and a remainder (whatever's left over) — the identical relationship long division relies on in decimal, just carried out here with numbers that happen to fit within 4 bits (0 to 15). Both the quotient and the remainder are then converted into their own binary digits, the same conversion this site's Binary Calculator applies to any whole number.
The relationship dividend = divisor × quotient + remainder always holds, and checking it is a quick way to confirm a division was done correctly — multiply the quotient back by the divisor, add the remainder, and the original dividend should reappear exactly.
Since the divisor here is always at least 1, division by zero never comes up — a case this page deliberately avoids, since dividing by zero has no defined result in any number base.
- Enter the dividend (0 to 15) into the Dividend field.
- Enter the divisor (1 to 15) into the Divisor field.
- Read the four Quotient bit fields and the four Remainder bit fields.
- Multiply the divisor by the quotient, add the remainder, and confirm the total reproduces the original dividend.
Worked example — 13 divided by 4
13 (1101) divided by 4 (0100) gives a quotient of 3 (0011) with a remainder of 1 (0001) — 4 fits into 13 exactly three whole times (4×3=12), with 1 left over. Checked in reverse: 4×3+1=13, confirming both results.
15 (1111) divided by 3 (0011) gives a quotient of 5 (0101) with no remainder at all (0000), an exact division. 7 (0111) divided by 8 (1000) gives a quotient of 0 (0000), with the entire dividend, 7 (0111), carried over as the remainder, since 7 is smaller than the divisor and can't fit even once.
Questions
What is the relationship between the dividend, divisor, quotient, and remainder?
Dividend = divisor × quotient + remainder, always — checking this relationship after a division is a quick way to confirm both the quotient and the remainder came out correctly.
What happens when the dividend is smaller than the divisor?
The quotient comes out to 0, and the entire dividend becomes the remainder instead — the divisor simply doesn't fit even once, exactly as it wouldn't in decimal division.
Can the remainder ever equal or exceed the divisor?
No — by definition, a proper remainder always stays strictly smaller than the divisor; if it reached the divisor's own size, the quotient would simply be one larger and the remainder would reset below it.
Why doesn't this page allow dividing by 0?
Division by zero has no defined result in any number base — the divisor field is restricted to start at 1 specifically to keep every division on this page well-defined.
How is this different from the Binary Calculator page on this site?
That page converts a single whole number into binary directly; this page first divides two numbers in ordinary arithmetic, then converts both resulting pieces, the quotient and the remainder, into binary separately.