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Binary, denary and hex converter

Convert from

Up to 8 bits for GCSE (16 at most), e.g. 1001 0110

Binary to denary

150 in denary

1001 0110 in binary is 150 in denary and 96 in hex.

Denary
150
Binary
1001 0110
Hex
96
1001 0110 = 150 = 96 in hex
1286432168421
10010110

Working

  1. Write the place values over the bits, doubling from the right: 128, 64, 32, 16, 8, 4, 2, 1.
  2. Add the place values that have a 1 under them: 128 + 16 + 4 + 2 = 150.
  3. Split the bits into groups of 4 (nibbles): 1001 0110. Each nibble is one hex digit: 1001 = 9, 0110 = 6. So the hex is 96.

Your result

150 in denary. 1001 0110 in binary is 150 in denary and 96 in hex.

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Binary 1001 0110 is 128 + 16 + 4 + 2 = 150 in denary and 96 in hex: each group of 4 bits is one hex digit.

Questions people ask

What is 255 in binary and hex?

255 is 1111 1111 in binary and FF in hex: every one of the 8 bits is 1. It is the largest number 8 bits can hold, which is why GCSE questions stop there.

Why do programmers use hex instead of binary?

Hex is shorter and easier to read: each hex digit stands for exactly 4 bits, so 1001 0110 becomes 96. It is quicker to write and fewer mistakes creep in, but the computer still stores binary.

How do I convert hex to binary quickly?

Turn each hex digit into its own 4 bits and put them side by side. 5A is 5 = 0101 and A = 1010, so 0101 1010. No denary step is needed.

What does a 0 at the start of a binary number do?

Nothing to its value: 0001 0110 and 1 0110 are both 22. Exam answers usually show all 8 bits, so keep leading zeros when the question asks for an 8-bit answer.

Keep going

How we work this out

What it does

Convert between binary, denary and hexadecimal, with the place values and nibbles shown the way GCSE mark schemes expect.

Whole numbers from 0 to 65,535 (16 bits). GCSE questions use 0 to 255, which is 8 bits or 00 to FF in hex.

Method

  1. Binary to denary: write the place values 128, 64, 32, 16, 8, 4, 2, 1 over the bits and add the ones with a 1 under them.
  2. Denary to binary: go from the largest place value, writing 1 and subtracting when it fits and 0 when it does not.
  3. Binary to hex: split the bits into groups of 4 (nibbles); each nibble is one hex digit from 0 to F.
  4. Hex to denary: multiply the first digit by 16 and add the second (A = 10 up to F = 15).