What is 0xFF in decimal?

255. F is 15, so FF = 15 × 16 + 15 = 240 + 15 = 255. The 0x at the start just means the number is in hex.

How do you convert hex to binary?

Write each hex digit as four binary digits: 0 = 0000, 9 = 1001, A = 1010, F = 1111. So 3C = 0011 1100.

Why do computers use hexadecimal?

Because one hex digit matches four bits exactly, hex is a short, readable way to write binary. Two hex digits make one byte.

64. 100 ÷ 16 = 6 remainder 4, and 6 ÷ 16 = 0 remainder 6, so reading up it's 64. Check: 6 × 16 + 4 = 100.

Is the calculator limited in size?

It handles whole numbers up to 40 digits long in any of the four bases, exactly, with no rounding.

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Hex to decimal calculator: hexadecimal, binary and octal, with steps

Type a number in hexadecimal, decimal, binary or octal and see it in all four bases at once. The steps show the place values for converting to decimal, and the divide-and-remainder method for converting back.

Convert from

Hexadecimal numberDigits 0 to 9 and A to F. Whole numbers up to 40 digits.

Binary (base 2)

10 1111

Octal (base 8)

Decimal (base 10)

Hexadecimal (base 16)

Steps: hexadecimal to decimal

Number the places from the right, starting at 0. Each place is worth 16 times the one to its right (powers of 16).
2 × 16¹ = 2 × 16 = 32
F (= 15) × 16⁰ = 15 × 1 = 15
Add them up: 47.

Steps: hexadecimal to binary

The quick way: each hex digit is exactly 4 binary digits.
2 = 0010
F = 1111
Put them together: 10 1111.

What hexadecimal is

Our everyday numbers are base 10: each place is worth ten times the place to its right, and we use the digits 0 to 9. Hexadecimal, or hex, is base 16. It needs sixteen digits, so after 9 it uses letters: A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15.

Computers use hex as a short way to write binary. Each hex digit stands for exactly four binary digits (bits), so the byte 1111 0101 is simply F5. That's why web colors look like #FF8800, and why memory addresses are written in hex.

How to convert hex to decimal

Number the places from the right, starting at 0.
Multiply each digit by 16 to the power of its place: 1, 16, 256, 4,096 and so on.
Turn letters into their values first: A is 10, F is 15.
Add up the results.
Example: 2F = 2 × 16 + 15 × 1 = 32 + 15 = 47.

How to convert decimal to hex

Divide the number by 16 and write down the remainder.
Divide the answer by 16 again, and keep going until the answer is 0.
Turn any remainder from 10 to 15 into its letter.
Read the remainders from the bottom up.
Example: 300 ÷ 16 = 18 r 12 (C), 18 ÷ 16 = 1 r 2, 1 ÷ 16 = 0 r 1. Reading up: 12C.

Binary and octal

Binary is base 2, with only the digits 0 and 1, and its place values are 1, 2, 4, 8, 16 and so on. Octal is base 8. The same two methods work for any base: multiply by powers of the base to get to decimal, and divide by the base to get back.

Questions people ask

What is 0xFF in decimal?: 255. F is 15, so FF = 15 × 16 + 15 = 240 + 15 = 255. The 0x at the start just means the number is in hex.
How do you convert hex to binary?: Write each hex digit as four binary digits: 0 = 0000, 9 = 1001, A = 1010, F = 1111. So 3C = 0011 1100.
Why do computers use hexadecimal?: Because one hex digit matches four bits exactly, hex is a short, readable way to write binary. Two hex digits make one byte.
What is 100 in hex?: 64. 100 ÷ 16 = 6 remainder 4, and 6 ÷ 16 = 0 remainder 6, so reading up it's 64. Check: 6 × 16 + 4 = 100.
Is the calculator limited in size?: It handles whole numbers up to 40 digits long in any of the four bases, exactly, with no rounding.

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