Converting Between Decimal & Hexadecimal (AQA GCSE Computer Science)

How do you convert decimal to hexadecimal?

Method 1 (decimal to binary to hexadecimal) 

• To convert the decimal number 28 to hexadecimal, start by converting the decimal number to binary

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

• Split the 8 bit binary number into two 4 bit numbers (nibbles) as shown below

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

• Convert each nibble to its decimal value
• 0001 = 1 and 1100 = 12
• Using the comparison table, the decimal value 1 is also 1 in hexadecimal whereas the decimal value 12 is represented in hexadecimal as C
• decimal 28 is 1C in hexadecimal

Method 2 (divide by 16)

• To convert the decimal number 163 to hexadecimal, start by dividing the decimal value by 16 and recording the whole times the number goes in and the remainder
• 163 ➗16 = 10 remainder 3
• In hexadecimal the whole number = digit 1 and the remainder = digit 2
• Digit 1 = 10 (A)
• Digit 2 = 3
• Decimal 163 is A3 in hexadecimal

How do you convert hexadecimal to decimal?

Method 1 (hexadecimal to binary to decimal)

• To convert the hexadecimal number B9 to decimal, take each hexadecimal value and convert it as decimal to 4 bit binary

B (11)					9
8	4	2	1		8	4	2	1
1	0	1	1		1	0	0	1

• Join the two nibbles to make an 8 bit number (byte)
• Convert from binary to decimal

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

• (1 x 128) + (1 x 32) + (1 x 16) + (1 x 8) + (1 x 1) = 185
• Hexadecimal B9 is 185 in decimal

Method 2 (multiply by 16)

• To convert the hexadecimal number 79 to decimal, start by multiplying the first hexadecimal digit by 16
• 7 ✖ 16 = 112
• Add digit 2 to the result
• 112 + 9 = 121
• Hexadecimal 79 is 121 in decimal