How to use
- In “Convert between bases”, type a number and pick its base. The binary, octal, decimal and hexadecimal values appear right away. Pick any other base from 2 to 36, such as base 3 or base 36, to see that value too.
- Letters are not case-sensitive, and spaces and underscores (_) are ignored. You can keep the prefix that matches the chosen base: 0b for binary, 0o for octal and 0x for hex.
- In “Calculate in a base”, choose binary, octal, decimal or hex, enter two numbers and pick an operation. The result is shown in that base and in decimal. Division shows the quotient and the remainder.
- Binary results are grouped in fours from the right for readability. Spaces are ignored, so you can copy a grouped value and paste it back in unchanged.
How base conversion works
- In base N, the digits from the right are worth 1, N, N², N³ and so on. Decimal 352 = 3×100 + 5×10 + 2×1, and every other base is read the same way.
- Base N to decimal: multiply each digit by its place value and add the results. 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11
- Decimal to base N: divide by N repeatedly until the quotient is 0, then read the remainders from the last one to the first.
- Hex uses 0–9 and then A (10) to F (15); base 36 uses letters all the way to Z (35). 2AF₁₆ = 2×256 + 10×16 + 15 = 687
- Four binary digits make one hex digit and three make one octal digit, so converting between binary and hex or octal is just grouping. 1111 1111₂ = 377₈ = FF₁₆ = 255
Step by step: decimal 200 to binary and hex
- Step 1, divide by 2: 200 ÷ 2 = 100 r 0, 100 ÷ 2 = 50 r 0, 50 ÷ 2 = 25 r 0, 25 ÷ 2 = 12 r 1
- Step 2, keep going until the quotient is 0: 12 ÷ 2 = 6 r 0, 6 ÷ 2 = 3 r 0, 3 ÷ 2 = 1 r 1, 1 ÷ 2 = 0 r 1
- Step 3, read the remainders from the last one up: 11001000, so 200 = 1100 1000₂.
- Step 4, group the binary digits in fours: 1100 = C and 1000 = 8, so the hex value is C8. Grouped in threes (11, 001, 000) it gives octal 310.
- Check: C8₁₆ = 12×16 + 8 = 200 and 310₈ = 3×64 + 1×8 + 0 = 200
Calculation examples
- 1010₂ + 0110₂ = 1 0000₂ (in decimal, 10 + 6 = 16)
- 1111₂ ÷ 100₂ = quotient 11₂, remainder 11₂ (in decimal, 15 ÷ 4 = 3 remainder 3)
- 1100₂ AND 1010₂ = 1000₂, OR gives 1110₂ and XOR gives 110₂ (8, 14 and 6 in decimal)
- A5₁₆ XOR FF₁₆ = 5A₁₆ (in decimal, 165 XOR 255 = 90). XOR with FF flips all of the lowest 8 bits.
- FF₁₆ + 1 = 100₁₆ (in decimal, 255 + 1 = 256)
Good to know
- Negative numbers keep their sign (−5 → −101₂). For an 8-bit two’s complement form, convert 256 − 5 = 251 to get 1111 1011₂ (FB₁₆); for 16 bits, convert 65536 − 5 = 65531 (FFFB₁₆).
- A prefix is removed only when it matches the chosen base. With hex selected, 0b11 is read as B11₁₆ (2833 in decimal), so pick binary before entering a binary value.
- Division rounds the quotient toward zero, and the remainder takes the sign of the first number: −7 ÷ 2 = quotient −3, remainder −1.
- Only integers are accepted, and a decimal point triggers a message saying so. There is no digit limit, so very long numbers are handled exactly.
Frequently asked questions
How do I convert binary to decimal?
Choose binary in “Convert between bases” and type the number; the decimal value appears instantly. By hand, multiply the digits from the right by 1, 2, 4, 8 and so on and add them up, so 1011₂ = 8 + 2 + 1 = 11.
How do I convert decimal to hexadecimal?
Divide by 16 repeatedly and read the remainders in reverse. 200 ÷ 16 = 12 r 8 and 12 ÷ 16 = 0 r 12 (C), so 200 = C8₁₆.
What is hex FF in decimal?
FF in hex is 255 in decimal. F stands for 15, so FF₁₆ = 15×16 + 15 = 255, which is 1111 1111 in binary.
Can I convert negative numbers?
Yes, put a minus sign in front and the sign is kept, as in −FF₁₆ = −255. The converter does not produce fixed-width two’s complement forms such as 8-bit or 16-bit values; for those, convert the value subtracted from a power of 2, such as 256 − 5 = 251.
How do AND, OR and XOR work with negative numbers?
Negative numbers are treated as two’s complement with an endless run of 1s on the left. For example, −5 AND 3 = 3 and −1 XOR 5 = −6, and a note under the result explains this.
Can I convert numbers with a decimal point?
No, only integers are supported. In return there is no digit limit, so even very long integers are converted exactly.
What bases are supported?
Any base from 2 to 36 can be converted. Digits above 9 are the letters A (10) to Z (35), so ZZ₃₆ = 1295, and calculations work in binary, octal, decimal and hex.