1. Binary and Decimal Numbers
CSCI-N 100
Dept. Computer & Information Science

2. Numbers in computers Originally designed to crunch numbers
Eckert and Mauchly (and scores more)
Univ. Penn, Moore School of Elec. Eng. (and lots of other places)
Long- range firing solutions in WW II (and other problems)
ENIAC (and many more machines and devices)

3. Power in the numbers Electrical power into computer
Series of switches opening and closing
Converts analog into digital (self-correcting switches make it high accurate digital device)

4. The divided machine Analog Digital
Nearly infinite in precision but limited accuracy
Digital
Limited precision but strongly accurate 1 on
High
Low
Off

5. What the computer doesn’t understand
Letters
Graphics
Colors
Characters
Sound
Other types of data

6. Making the computer understand
Convert what we know to something the computer understands
Converting analog to digital
Switches opening and closing
Open On
Closed Off

7. Making the user understand
Computer sending back information to the user
Converting the 1s and 0s into something the user understands

8. Representation Calendar Time Temperature
Represents movement of the Earth around the Sun
Time
Represents a given amount of movement of the Earth
Clock
Temperature
Represents
Sun’s ray reflecting of Earth surface
Interaction of reflective rays with molecule in the atmosphere
Excited molecules generate heat
Thermometer

9. The Numbers Binary – Base 2 Decimal – Base 10 Other number bases 0, 1
0 – 9
Other number bases
Octal – Base 8 (0 – 7)
Hexadecimal – Base 16 (0 – 9, a – f)

10. How the computer deals with numbers
Real numbers (infinite) Pi
1/3 (.3333)
Not enough computer memory
Infinitely precise
Uses round-off error (also called floating point)

11. Sound, Graphics, Text? Not represented in a ‘natural’, numeric way
Need to convert bits of information from analog to ‘digital information’

12. Representing text Text represented by ASCII
Original ASCII 7-bit character (27 = 128)
Extended ASCII 8-bit character (28 = 256)
Uses Western European English character set
UNICIODE
65,000 character set coding scheme
Used for languages that use glyphs
Chinese
Arabic
Hebrew
EBCDIC 8-bit code

13. Representing graphics
Pixel
Dot on in the image assigned numeric value
Translate to monitor
Graphics use hexadecimal coding for use in web pages on the Internet
Red Green Blue (RRGGBB)
GIF, JPG, PNG, BMP, TIF (and lots more)

14. Representing sound MIDI (developed 1982 my music industry)
AU (supported by many different software systems over a large range of platforms)
RealAudio (developed by Real Media for Internet use)
AIFF (developed by Apple)
SND (developed by Apple)
MP3 (developed by Moving Pictures Experts Group)
WAVE (developed by IBM and Microsoft)

15. Base 10 to Base 2 28 27 26 25 24 23 22 21 20
256
128 64 32 16 8 4 2 1
Find the binary number that is EQUAL TO BUT LESS THAN the decimal number, SUBTRACT
– 4 = 2
230 – 128 = – 2 = 0
102 – 64 = =
38 – 32 = 6
6 – 16, cannot subtract
6 – 8, cannot subtract

16. Base 2 to Base 10 28 27 26 25 24 23 22 21 20
256
128 64 32 16 8 4 2 1
ADD the BINARY switches turned on, reading left to right =
256
+128
+64
+32 +0 +4 +2