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Number Systems - Binary, Decimal & Hexadecimal

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Alun King

on 7 October 2013

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Transcript of Number Systems - Binary, Decimal & Hexadecimal

Number Systems - Binary, Decimal & Hexadecimal
Decimal Numbers
We are most familiar with Decimal numbers. (0 - 9)
Can you remember how they work? (primary school style)

Our numbers are laid out in columns. Each column is 10x bigger from left to right.

100,000's 10,000's 1000's 100's 10's 1's

e.g. 45256 = 4 x 10,000, 5 x 1000, 2 x 100, 5 x 10, 6 x 1
Binary Numbers
Work exactly like decimal numbers, but we only have two digits.

columns are 2x bigger from right to left

32 16 8 4 2 1

so 100101 = 1x32 + 4x1 + 1x1

32 + 4 + 1 = 37 (in decimal)

Hexadecimal Numbers
Hexadecimal numbers have 16 values (0 - F)

Letters represent double digit numbers to avoid confusion

Columns go up by 16

256's 16's 1's

Converting & Notation
Converting Decimal to Binary or Hex is hard work. You need to use the tables

Converting from Binary to Hexedecimal & back is easy

To tell the difference between bin, dec and hex, put a B, D or H after the number.
You might be wondering why these numbers exist. OK, binary and decimal are understandable but why Hex?

Hex is shorthand binary - FFF is quicker and easier to write (and read) than 111111111111.

It makes binary easier to read for humans.
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