How this instrument works
Just as whole-number binary places grow by doubling moving leftward (ones, twos, fours, eights), binary places AFTER the point shrink by halving moving rightward: the first place is worth one half, the next one quarter, the next one eighth, and the next one sixteenth. A binary fraction like 0.1010 converts to decimal by adding up whichever of those halving place values have their bit switched on.
This mirrors the whole-number conversion this site's Binary Calculator performs, just running in the opposite direction across the point — shrinking place values instead of growing ones, but built from the identical doubling relationship that defines binary in the first place.
The largest possible value four fractional bits can reach is 0.9375 (every bit switched on: 0.5+0.25+0.125+0.0625), always falling just short of a full 1 — adding a fifth bit would close that gap further, but never quite reach it with any fixed number of bits.
- Enter each of the four fractional bits (0 or 1) into their own field, from the halves place down to the sixteenths place.
- Read Decimal value: the sum of whichever place values have their bit switched on.
- Try all four bits off, then all four on, to see the full range this page can convert.
- Compare against this site's Binary Calculator, which converts whole numbers using the identical doubling idea, just growing instead of shrinking.
Worked example — converting 0.1010
The binary fraction 0.1010 has its first and third bits switched on: 0.5 (from the first bit) plus 0.125 (from the third bit) totals 0.625, with the second and fourth bits (worth 0.25 and 0.0625) both off, contributing nothing.
0.0000, every bit off, converts to exactly 0. 0.1111, every bit on, converts to 0.5+0.25+0.125+0.0625=0.9375 — the largest value four fractional bits can reach, always just shy of a full 1.
Questions
How do binary place values work after the point?
They shrink by half moving rightward — one half, one quarter, one eighth, one sixteenth — the mirror image of whole-number binary places, which double moving leftward instead.
What is the largest value four fractional bits can represent?
0.9375, with every bit switched on — always just short of a full 1, since a fixed number of binary fractional bits can approach but never exactly reach the next whole number this way.
How is this different from the Binary Calculator page on this site?
That page converts a whole number into binary, with places that GROW moving leftward; this page converts a binary fraction into decimal, with places that SHRINK moving rightward, past the point.
Can every decimal fraction be represented exactly in binary?
No — some decimal fractions, like 0.1, actually repeat forever in binary, the same way some fractions like 1⁄3 repeat forever in decimal; only fractions built from halves, quarters, eighths, and so on convert exactly with a finite number of bits.
What does a fractional bit of 0 contribute?
Nothing — a bit switched off contributes exactly 0 to the total, regardless of what place value it would otherwise carry, exactly as an off bit contributes nothing on the whole-number side of the point.