1. How to Represent Numbers on a Computer
Digital Data
How to Represent Numbers on a Computer

2. Memory: One Bulb On=Yes Off=No
Memory is made up of two-state devices, like a light bulb. One bulb has two states. We could store two things (yes or no).
On=Yes
Off=No

3. Two bulbs, four states: Off, off: Off, on: On, off: On, on: No, no
No, yes
Yes, no
Yes, Yes

4. Three bulbs, eight states:
Off, off, off
Off, off, on
Off, on, off
Off, on, on
On, off, off
On, off, on
On, on, off
On, on, on

5. Four bulbs, 16 states:

6. Pretend they are numbers, where off=0 and on=1:
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

7. How do we interpret the numbers?
Base 10 numbers:
10 digits: 0 through 9
Place value is based on powers of 10
___ ___ ___ ___ ___ ___
100, , ,

8. Base 10
100, , ,
So 123,456 =
1 * 100,000 = 100,000
2 * 10,000 = ,000
3 * 1,000 = ,000
4 * 100 =
5 * 10 =
6 * 1 =
123,456

9. With 2 digits: Base 2 number system: __ __ __ __ __ __ __ __
2 digits: 0 through 1
Place value is based on powers of 2
__ __ __ __ __ __ __ __

10. Base 2
__ __ __ __ __ __ __ __ So = 1 * 128 = * 64 = 0 1 * 32 = 32 0 * 16 = 0 1 * 8 = 8 0 * 4 = 0 1 * 2 = 2 0 * 1 = 0 170

11. The first 8 binary numbers (with leading zeros)
0000= = = = = = = = = = = = = = = = 7

12. Binary numbers are represented in BYTES – groups of 8 bits
Byte: a group of 8 bits. The basic unit of storage on most computers. 0 = = = = = = = =

13. Some other binary numbers
= = = = = = = 255

14. Need numbers greater than 255?
Use two bytes: Smallest number = Biggest number = = , ,768 = 65,535

15. Need numbers greater than 65,535?
Use 4 bytes: Smallest number: Biggest number: = 4,294,967,295

16. Other numbers There are also ways to represent:
Decimal fractions
Negative numbers
These will be covered elsewhere.

17. The End