Binary Numbers Explained: Converting To and From Decimal
Binary (base 2) uses just two digits — 0 and 1 — yet it underpins every computer. Understanding it demystifies a lot of how computing works.
How binary place values work
In decimal, each place is a power of 10. In binary, each place is a power of 2: 1, 2, 4, 8, 16, 32… So 1011 = 8 + 0 + 2 + 1 = 11 in decimal. Reading right to left, you just add the place values where there's a 1.
Decimal to binary
Repeatedly divide the number by 2 and record the remainders, then read them bottom-up. 11 ÷ 2 = 5 r1, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1 → 1011.
Convert instantly
Our free decimal to binary and binary to decimal converters handle it both ways. To see how it all fits together, read our number systems guide.
Bottom line
Binary place values are powers of 2 — add them up where there's a 1 to get decimal, or divide-by-2-and-collect-remainders to go the other way. Once the place-value idea clicks, binary stops being mysterious.
