1. COMS 161 Introduction to Computing
Title: Digital Numbers
Date: January 28, 2005
Lecture Number: 8

2. Announcements
Why do sea-gulls fly over the sea? Because if they flew over the bay they would be bagels!
A man left home running. He ran a ways and then turned left, ran the same distance and turned left again, ran the same distance and turned left again. When he got home there were two masked men. Who were they? A catcher and an umpire

3. Review Numbers Non-positional Positional Decimal Octal Binary
Definition
Decimal
Octal
Binary

4. Outline
Numbers
Unsigned and signed

5. Binary number system Digital and binary relationship
The language of computers use binary digits
Only 2 possible values
0 and 1
Much simpler to make electronics that distinguish between one of two values
Distinguishing between more than two values is very difficult

6. Binary number system Since binary digits have two possible values
Binary digits are called bits
They only contain a little “bit” of information
Numbers represented in binary form will (most likely) require more digits (bits) than the decimal form

7. Binary Number System How many values can 2 bits represent? Bit Pattern
Numeric Value
Item Represented 00
Black 01 1
White 10 2
Red 11 3
Green

8. Binary Number System How many values can 3 bits represent? Bit Pattern
Numeric Value
Item Represented
000
Black
001 1
White
010 2
Red
011 3
Green
100 4
Blue
101 5
Purple
110 6
Magenta
111 7
Sky blue

9. Binary Number System How many values can 4 bits represent? Bit Pattern
0000
1000 8
0001 1
1001 9
0010 2
1010 10
0011 3
1011 11
0100 4
1100 12
0101 5
1101 13
0110 6
1110 14
0111 7
1111 15

10. Binary Number System
Bit patterns and numeric values are consistent with other slides
Acceptable to add leading 0’s if desired

11. Binary number system
Possible to represent more information than that of a single bit
Lump together multiple bits called strings
One bit: 2 values
Two bits: 4 values (00, 01, 10, 11)
Three bits: 8 values (000, 001, …, 111)
Four bits: 16 values (0000, …, 1111)
Five bits: 32 values
Six bits: 64 values
Seven bits: 128 values
Eight bits: values

12. Binary number system number of values = 2number of bits In general
1 = 20
2 = 21
4 = 22
8 = 23
16 = 24
32 = 25
64 = 26
128 = 27
256 = 28

13. Binary number system Common bit grouping’s
4 bits: nibble
8 bits: byte
One byte represents 256 different values or items