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Conversions Denary to Binary Method 1

Conversions Denary to Binary Method 1 Divide the number repeatedly by two and note the carry. For example 178 to binary 178 / 2 = 89 reminder 0 89 / 2 = 44 remainder 1 44/2 = 22 remainder 0 22/2 = 11 remainder 0 11/2 = 5 remainder 1 5/2 = 2 remainder 1 2/2 = 1 remainder 0

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Conversions Denary to Binary Method 1

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  1. Conversions Denary to Binary Method 1 Divide the number repeatedly by two and note the carry. For example 178 to binary 178 / 2 = 89 reminder 0 89 / 2 = 44 remainder 1 44/2 = 22 remainder 0 22/2 = 11 remainder 0 11/2 = 5 remainder 1 5/2 = 2 remainder 1 2/2 = 1 remainder 0 1 = 1 So starting from the bottom 178 is 10110010 in binary

  2. Conversions Denary to Binary Method 2 Set out the binary positions and if the number – that position is a positive – put a 1 in it. For example 178 – 128 = 50 – so 1 in the 128 position 50 – 64 = -14 so a 0 in the 64 position 50 – 32 = 18 so 1 in the 32 position

  3. Conversions Denary to Binary Method 2 18-16 = 2 so 1 in the 16 position 2-8 = -6 so 0 in the 8 position 2-4 = -2 so 0 in the 4 position 2-2 = 0 so 1 in the 2 position Leaving 0 in the 1 position

  4. Conversions Binary to Denary Method 1 Work out the position values of the binary bits and add those values together So above would be 128 + 32 + 16 + 2 = 178

  5. Conversions Denary to hexidecimal Method 1 Divide the number repeatedly by 16 until you have a number less than 16. For example: 178 / 16 = 11 remainder 2 So 2 becomes B2 1076 / 16 = 67 remainder 4 67 / 16 = 4 remainder 3 4 = 4 So 1076 is 434 in hexadecimal.

  6. Conversions Denary to hexidecimal Method 2 Each number of a hexadecimal converts to 4 bits so you could work out the denary number in binary first then split it into 4 bits and work out the hex numbers from that. 1076 = Now split into 4s And work out the value of each 4 bits separately. 0100 = 4 0011 = 3 0100 = 4

  7. Conversions Hexidecimal to Denary Method 1 Each unit of a Hex number is going to be a power of 16 so you just multiple each number by that power and add them together. So AF9 is So this will be (10 * 256) + (15*16) + (9*1) = 2560 + 240 + 9 = 2809

  8. Conversions Hexidecimal to Denary Method 2 Convert the number to binary by just taking each unit as four bits and then do a binary to denary conversion So AF9 is Then convert that back to denary = 2048 + 512 + 128 + 64 + 32 + 16 + 8 + 1 = 2809

  9. Conversions Binary to Hexidecimal and back again Method 1 Split the Binary number into 4 bits each and each four bits then represents a single hexadecimal number, for example: 111011010011 To convert from Hex back to binary you just reverse the procedure.

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