1. Binary numbers: Week 7 Lesson 1

2. Humans count using denary numbers (base 10).
We use 10 units: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
103
102
101
100
1000 10 1 5 4 9
(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. 23 22 21 20 8 4 2 1
(1 x 8 = 8) 8
(1 x 4 = 4) + 4
(0 x 2 = 0) + 0
(1 x 1 = 1) + 1
=13

3. Binary to denary
Binary
Denary 8 4 2 1

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

5. And with 8 bits (a byte) you can represent 256 different numbers: 0 to 25527 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
(1 x 128)
(1 x 64)
(1 x 32)
(0 x 16)
(1 x 8)
(1 x 4)
(0 x 2)
(1 x 1)
+ 64
+ 32
+ 0
+ 8
+ 4
+ 1
= 237

6. How to… convert from binary to denary:
Add up the column values for each ‘1’, e.g.
1110 = = 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 number you don’t use, e.g.
29 = 29 – 16 = 13 – 8 = 5 – 4 = 1 – 1 = 0

7. Binary arithmetic: Week 9 Lesson 1