课 14, 主题 2

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Converting Between Decimal And Hexadecimal Aqa

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Exam code:8525

Decimal to Hexadecimal Conversion

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

Table showing binary representation of the decimal number 30, with bit values 00011110 from left to right under the place values 128, 64, 32, 16, 8, 4, 2, 1.

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

Two rows of binary numbers are separated by a black bar. The top row contains values 8, 4, 2, and 1 in blue. The bottom row displays 0s and 1s in red.

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

Hexadecimal to Decimal Conversion

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

Table showing binary representations. Number 11 in blue; below it, digits 8, 4, 2, 1 with values 1, 0, 1, 1 in red. Number 9 in blue; below it, digits 8, 4, 2, 1 with values 1, 0, 0, 1 in red.

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

A binary table with columns labeled 128, 64, 32, 16, 8, 4, 2, and 1. Below, the binary representation is 00011100.

(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

Examiner Tips and Tricks

Remember that the exam is non-calculator, if you are not confident multiplying and dividing by 16 then use method 1 on both conversions

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