Converting Between Hexadecimal & Denary (CIE IGCSE Computer Science)

Converting Denary to Hexadecimal Walkthrough:

1. Divide the decimal number (in this example 57) by 16 and write down the answer including the remainder:
   57 ÷ 16 = 3 remainder 9
2. If the remainder is above 9, replace this with the corresponding letter
3. Repeat steps 1 and 2 until the number you’re dividing is zero:
   3 ÷ 16 = 0 remainder 3
4. Write the hexadecimal values from step 3 to step 1 in reverse order:
   39

Alternatively, you can turn your denary number into binary, and then turn the binary number into hexadecimal:

1. Work out 57 in binary

128	64	32	16	8	4	2	1
0	0	1	1	1	0	0	1

2. Split it into 2 nibbles

8	4	2	1		8	4	2	1
0	0	1	1		1	0	0	1

3. Turn each nibble into its hex value

2+1=3                                 8+1=9

Answer is 39

Converting Hexadecimal to Denary Walkthrough:

• Write down the place value of each digit in the number, starting from the right and increasing by a power of 16:
  
  

  161	160
  16	1

• If the hex digit is a letter, convert it to its denary equivalent (Using the following table to help you):
  

Hexadecimal	Decimal
A	10
B	11
C	12
D	13
E	14
F	15

• The hexadecimal value of the leftmost digit E has a decimal value of 14. The hexadecimal value of the rightmost digit is 5, which has a decimal value of 5
  

  16	1
  E	5

• Multiply each decimal value by its corresponding place value, and sum the products:

(14 x 16) + (5 x 1) = 224 + 5 = 229

Therefore, the denary equivalent of E5 is 229.

Alternatively, you can turn your hexadecimal number into binary, and then turn the binary number into denary:

1. Write each hex digit in binary

8	4	2	1		8	4	2	1
1	1	1	0		0	1	0	1

2. Convert the binary to denary

128	64	32	16	8	4	2	1
1	1	1	0	0	1	0	1

128+64+32+4+1=229