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Converting between hex and binary

Introduction
In the previous section, we saw how to convert between decimal numbers and hex. We did this by using a trick to do the conversion. We converted our decimal number into binary first and then into hex. We are using the fact that a hex number is simply a group of 4 binary bits (and a group of 4 bits is called a nibble) .

To convert a binary number into hex, use these weightings for each bit in the nibble:

Example 1 - convert 0010 1010 into hex.

• • Each group of four bits is a hex number.
  • 0010 is 2 in denary, which is 2 in hex.
  • 1010 is 10 in denary, which is A in hex.
  • Putting the hex digits together, we have 0010 1010 in binary is 2A in hex.

Example 2 - convert 0011 1110 into hex.

• • Each group of four bits is a hex number.
  • 0011 is 3 in denary, which is 3 in hex.
  • 1110 is 14 in denary, which is E in hex.
  • Putting the hex digits together, we have 0011 1110 in binary is 3E in hex.

Example 3 - convert 0110 0000 into hex.

• • Each group of four bits is a hex number.
  • 0110 is 6 in denary, which is 6 in hex.
  • 0000 is 0 in denary, which is 0 in hex.
  • Putting the hex digits together, we have 0110 0000 in binary is 60 in hex.

Example 4 - convert 1111 0100 into hex.

• • Each group of four bits is a hex number.
  • 1111 is 15 in denary, which is F in hex.
  • 0100 is 4 in denary, which is 4 in hex.
  • Putting the hex digits together, we have 1111 0100 in binary is F4 in hex.

To convert a hex number into binary, we just reverse the process. Treat each hex digit as its own 4 bit number.

Example 1 - convert 2B16 into binary.

• • Each hex digit is a standalone nibble.
  • 2 in hex is 0010 in binary.
  • B in hex is 1011 in binary.
  • Putting the nibbles together, we have 2B in hex is 0010 1011 in binary.

Example 2 - convert FF16 into binary.

• • Each hex digit is a standalone nibble.
  • F in hex is 1111 in binary.
  • F in hex is 1111 in binary.
  • Putting the nibbles together, we have FF in hex is 1111 1111 in binary.

Example 3 - convert 0D16 into binary.

• • Each hex digit is a standalone nibble.
  • 0 in hex is 0000 in binary.
  • D in hex is 1101 in binary.
  • Putting the nibbles together, we have 0D in hex is 0000 1101 in binary.

Example 4 - convert 4716 into binary.

• • Each hex digit is a standalone nibble.
  • 4 in hex is 0100 in binary.
  • 7 in hex is 0111 in binary.
  • Putting the nibbles together, we have 47 in hex is 0100 0111 in binary.

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