Computer Science · Data representation. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A computer is built from millions of tiny switches that are either on or off. So all data, whether numbers, text, sound or images, is stored as binary: patterns of 1s and 0s.
Denary uses place values 1, 10, 100. Binary uses 1, 2, 4, 8, 16, 32, 64, 128. Hexadecimal uses 16 digits, 0 to 9 then A to F (A = 10, F = 15). One hex digit stands for exactly four bits, so hex is shorter and easier for people to read than binary.
You must also add 8-bit numbers, shift them left or right, and write negative numbers in two's complement, where the left-most bit is worth −128.
Students read a hex digit such as C as a denary 12 and then forget to multiply by its place value. In 3C the 3 is worth 3 × 16, not 3.
Answer: 219 in denary is DB in hexadecimal.
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