Converting Between Hexadecimal & Denary | Computer for GCSE/IGCSE - Year 11 PDF Download

Converting Denary to Hexadecimal Walkthrough

• Start by dividing the decimal number (for instance, 57) by 16, noting both the quotient and the remainder: 57 ÷ 16 = 3 remainder 9.
• If the remainder surpasses 9, substitute it with the appropriate letter.
• Continue the process by dividing the quotient from the previous step by 16 until the number being divided reaches zero: 3 ÷ 16 = 0 remainder 3.
• Arrange the hexadecimal values obtained from the last step to the initial step in reverse order: 39.

You can convert your decimal number into binary first, then convert the binary number into hexadecimal:
1. Work out 57 in binary

2. Split it into 2 nibbles
3. Turn each nibble into its hex value
2 + 1 = 3, 8 + 1 = 9
Answer is 39

Converting Hexadecimal to Denary Walkthrough

• Begin by noting the place value of each digit in the number, starting from the right and increasing by a power of 16.

• If you encounter a hex digit that is a letter, refer to the conversion table to find its denary equivalent.

• The leftmost digit, such as 'E', holds a decimal value of 14. The rightmost digit, like '5', equates to a decimal value of 5.
  
• Multiply each decimal value by its corresponding place value and then sum up the products to get the final denary value.
• For instance, (14 x 16) + (5 x 1) = 224 + 5 = 229.
• Hence, the decimal equivalent of E5 is 229.

Alternatively, you can convert your hexadecimal number into binary, followed by converting the binary number into decimal:
1. Write each hex digit in binary
2. Convert the binary to denary
128 + 64 + 32 + 4 + 1 = 229