Convert hex to decimal and binary

Enter a number in one base and immediately get it in all the others. The hex number FF becomes 255 in decimal, 11111111 in binary, and 377 in octal. The calculator also shows the calculation and, if the number fits in 64 bits, every individual bit.

Each position in a hex number is a power of 16, counting from the right: 1, 16, 256, 4096. Multiply each digit by its place value and add the results; the letters A through F represent 10 through 15. This makes 2A equal to 2 × 16 + 10 × 1 = 42.

Add the place values of all the 1s. Counting from the right, they are 1, 2, 4, 8, 16, and so on. So the binary number 1101 is 8 + 4 + 1 = 13. Enter the binary number in the Binary field above to see each position in the calculation.

Keep dividing the number by 2 and note each remainder until you reach 0. Read the remainders from bottom to top to get the binary number: 42 becomes 101010. Converting decimal to octal works the same way with 8, and decimal to hex with 16.

Use repeated division by 16. Each remainder from 10 to 15 becomes a letter from A to F. Dividing 2026 by 16 gives 126 remainder 10 (A); 126 divided by 16 gives 7 remainder 14 (E); 7 divided by 16 gives 0 remainder 7. Reading from bottom to top, 2026 is 7EA.

No need to go through decimal: four bits make exactly one hex digit. Split the binary number into groups of four from the right and replace each group with its digit: 1010 1111 becomes AF. To go the other way, write each hex digit as four bits. The same works for octal using groups of three.

This is how computers store negative integers. With a fixed bit width, invert all the bits of the absolute value and add 1. With 8 bits, −1 becomes 11111111, or FF, and −128 becomes 10000000. Select two's complement and the bit width above to see the bit pattern and calculation.

Unsigned, FFFFFFFF is 4294967295, the largest 32-bit number. In 32-bit two’s complement, the same bit pattern represents -1. Select Two’s complement and 32 bits above, then enter FFFFFFFF in the Hexadecimal field: the Decimal field will show -1, while the bits will also show the unsigned value.

Integers in any base from 2 to 36, exact up to 1024 digits—even far beyond 64 bits. The prefixes 0x, 0b and 0o, as well as # for hex, are recognised. Spaces, underscores and apostrophes between digits are ignored. The converter doesn’t support fractional numbers; entering a comma or period in the Decimal field displays a notice.

The Binary Translator converts text—letters and characters—to binary code and back. This converter converts numbers between number bases: the number 65 becomes 1000001. To write a word in binary, use the Binary Translator. To convert a number, you're in the right place.