1. Binary numbers

2. 1 Humans count using decimal numbers (base 10) We use 10 units: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 10 3 10 2 10 1 10 0 1000100101 5049 (5 x 1000 = 5000) 5000 (0 x 100 = 0) + 0 (4 x 10 = 40) + 40 (9 x 1 = 9) + 9 =5049 Computers count using binary numbers (base 2) They use just 2 units: 0 and 1 23232 2121 2020 8421 1101 (1 x 8 = 8) 8 (1 x 4 = 4) + 4 (0 x 2 = 0) + 0 (1 x 1 = 1) + 1 =13

3. Binary numbers2 Binary to denary BinaryDenary 8421 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

4. Binary numbers3 Denary to binary BinaryDenary 8421 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

5. Binary numbers4 And with 8 bits (a byte) you can represent 256 different numbers: 0 to 255 2727 2626 2525 2424 23232 2121 2020 1286432168421 11101101 (1 x 128)(1 x 64)(1 x 32)(0 x 16)(1 x 8)(1 x 4)(0 x 2)(1 x 1) 128+ 64+ 32+ 0+ 8+ 4+ 0+ 1= 237

6. Binary numbers5 How to… convert from binary to denary Add up the column values for each ‘1’, e.g. 1110 = 8 + 4 + 2 = 14 convert from denary to binary Take away the largest power of two you can and put a 1 for each number you take away and a 0 for each numbers you don’t use, e.g. 29 = 29 – 16 = 13 – 8 = 5 – 4 = 1 – 1 = 0 0001 1101