Converting decimal to binary is a core skill for anyone learning how computers store numbers. Here are the two standard hand methods, both confirmed on a base-N calculator.
On this page
Place values
Each binary digit is a power of two, doubling from right to left:
... 64 32 16 8 4 2 1A binary number is just the sum of the place values where a 1 sits. So 1101 = 8 + 4 + 0 + 1 = 13.
The divide-by-2 method
Divide repeatedly by 2 and record remainders; read them bottom-to-top.
13 ÷ 2 = 6 r 1
6 ÷ 2 = 3 r 0
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1
read up → 110113 (decimal) = 1101 (binary). ✔
25 → remainders 1,0,0,1,1 → 11001 = 16 + 8 + 1 = 25. ✔
The subtract-powers method
Take the largest power of two that fits, subtract, repeat:
255 − 128 = 127 → bit 128 = 1
127 − 64 = 63 → bit 64 = 1 … and so on
result: 11111111255 = 11111111 (eight 1s). ✔
Straight to hex
Group the binary digits into fours from the right and convert each group:
1111 1111 → F F → FFThat four-bit grouping is why hexadecimal is so popular with programmers — see the binary, octal & hex calculator pillar guide.
On the calculator
Switch to BASE-N mode, enter 13 in DEC, then select BIN to read 1101 (or HEX for D). It's the fastest way to check any conversion. Negative values use two's complement — see the two's complement walkthrough.
Frequently asked questions
How do I convert decimal to binary?
Divide by 2 repeatedly and read the remainders bottom-to-top; 13 gives 1101.
How do I convert binary to hex?
Group the bits into fours from the right and convert each group; 1111 1111 = FF.
What are the binary place values?
Powers of two — 1, 2, 4, 8, 16, … — and you sum the ones that have a 1.
Check any conversion
Enter a number in BASE-N mode and switch bases to see binary, octal and hex.
Open the decimal to binary converter →