CPSC 171 Introduction to Computer Science

1. CPSC 171 Introduction to Computer Science Binary

2. Announcements • Read Chapter 4 • Lab 4 & 5 due tomorrow at beginning of Lab • Homework 3 due this Friday at beginning of Lecture • EXAM Friday October 2nd in class

3. Real World To be, or not to be: that is the question: Whether 'tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles, And by opposing end them? To die: to sleep; No more; and by a sleep to say we end The heart-ache and the thousand natural shocks That flesh is heir to, 'tis a consummation Devoutly to be wish'd. -- William Shakespeare - (from Hamlet Act 3, Scene 1) Computer World 101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111… Example Representation

4. Real World Integers: 34 Signed Integers: -156 Decimal Numbers:-23.431 Text: Hello Music: Hey Jude Pictures: Computer World Zeros and Ones:110101 Internal and External Representation of Data

5. Integer Representation • We use a base 10 number system (Decimal)0, 1, 2, 3, 4, 5, 6, 7, 8, 9 2,359 thousands hundreds ones tens 103 102 101 100 • Computers use a base 2 number system (Binary)0, 1 110101 25 24 23 22 21 20

6. Conversion from Binary to Decimal 110101 1x25+1x24+0x23+1x22+0x21+1x20=53 You Try it: What are the following binary numbers in decimal? 11011 101100 110111 25 24 23 22 21 20

7. Conversion from Decimal to Binary • Perform repeated divisions by 2 • Keep track of the remainders 19 / 2 quotient = 9 remainder = 1 9 / 2 quotient = 4 remainder = 1 4 / 2 quotient = 2 remainder = 0 2 / 2 quotient = 1 remainder = 0 1 / 2 quotient = 0 remainder = 1 • Stop when the quotient is 0 Decimal number 19 in binary is 10011 • You Try it Convert the following decimal numbers to binary 12 31 53

8. Addition on Binary • 0 + 0 = 0 • 1 + 0 = 1 • 0 + 1 = 1 • 1 + 1 = 10 (carry the 1) 1101 11010 +1001+10011

9. Fixed Sizes for Numbers • On computers a fixed number of digits are typically used to store a number(8, 16, 32, or 64 bits are common) • The decimal number 3 in binary is 11, but using a fixed size of 8 bits it would be represented as 00000011 • Try adding the binary numbers using a fixed size of 8 bits: 11011001 +10001011

10. Real World Integers: 34 Signed Integers: -156 Decimal Numbers:-23.431 Text: Hello Music: Hey Jude Pictures: Internal and External Representation of Data √

11. Signed Integers -134 • Sign/Magnitude Notation 110000110 magnitude • Not frequently used on computers • 2 numbers for zero • Not easy to add/subtract Sign 0 = positive 1 = negative

12. Signed Integers -134 • Two’s Complement Notation (for fixed size window 16) • Calculate the magnitude in binary0000000010000110 • Flip the bits1111111101111001 • Add one1111111101111010 • You Try it -129 -151

13. Real World Integers: 34 Signed Integers: -156 Decimal Numbers:-23.431 Text: Hello Music: Hey Jude Pictures: Internal and External Representation of Data √ √

14. Decimal Numbers 5.75 Write the 5 in binary and the 0.75 in binary 5 – 101 0.75 – 0.11 Normalize the number, keeping track of Mantissa and Exponent: ±MxB±E M – Mantissa B – Base (we use base 2) E – Exponent Used fixed size window (16 bits) First bit is sign Next 9 bits are Mantissa Next bit is sign Last 5 bits are Exponent You Try It: -8.25 11.5

15. Text • Fixed Size Window represents a character • ASCII (8 bits) pg 141 in text • Unicode (16 bits) represents 65,636 characters

16. Binary Representation of Sound and Images • Multimedia data is sampled to store a digital form with or without detectable differences • Representing sound data • Sound data must be digitized for storage in a computer • Digitizing means periodic sampling of amplitude values

17. Binary Representation of Sound and Images (continued) • From samples, original sound can be approximated • To improve the approximation • Sample more frequently • Use more bits for each sample value

18. Figure 4.5 Digitization of an Analog Signal (a) Sampling the Original Signal (b) Recreating the Signal from the Sampled Values

19. Binary Representation of Sound and Images (continued) • Representing image data • Images are sampled by reading color and intensity values at even intervals across the image • Each sampled point is a pixel • Image quality depends on number of bits at each pixel

20. For each pixel keep track of: RGB values 0-255 (8-bit) Pictures

21. Why Binary Representation • Electronic devices are most reliable in a bistable environment • Bistable environment • Distinguishing only two electronic states • Current flowing or not • Direction of flow • Computers are bistable: binary representations

22. Binary Storage Devices • Magnetic core • Historic device for computer memory • Tiny magnetized rings; flow of current sets the direction of magnetic field • Binary values 0 and 1 are represented using the direction of the magnetic field

23. Figure 4.9 Using Magnetic Cores to Represent Binary Values

24. Binary Storage Devices (continued) • Transistors • Solid-state switches; either permit or block current flow • A control input causes state change • Constructed from semiconductors

25. Figure 4.11 Simplified Model of a Transistor