CPSC 171 Introduction to Computer Science

Binary

Announcements

Read Chapter 4Lab 4 & 5 due tomorrow at beginning of LabHomework 3 due this Friday at beginning of LectureEXAM Friday October 2nd in class

Example Representation

Real WorldTo 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 World101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111101010001101111100000011000101010100011011001100110011000101110111011111100010101011010100010110111011000101010110001011011101001000100010101010111010101011011010010111…

Internal and External Representation of Data

Real WorldIntegers: 34Signed Integers: -156Decimal Numbers:-23.431Text: HelloMusic: Hey JudePictures:

Computer WorldZeros and Ones:110101

Integer RepresentationWe use a base 10 number system (Decimal)0, 1, 2, 3, 4, 5, 6, 7, 8, 9

2,359

tens

hund

reds

thou

sand

son

es

100

101

102

103

Computers use a base 2 number system (Binary)0, 1

110101

20

21

22

23

24

25

Conversion from Binary to Decimal

1x25+1x24+0x23+1x22+0x21+1x20=53

You Try it:What are the following binary numbers in

decimal?11011101100110111

110101 20

21

22

23

24

25

Conversion from Decimal to Binary

Perform repeated divisions by 2Keep track of the remainders

19 / 2 quotient = 9 remainder = 19 / 2 quotient = 4 remainder = 14 / 2 quotient = 2 remainder = 02 / 2 quotient = 1 remainder = 01 / 2 quotient = 0 remainder = 1

Stop when the quotient is 0Decimal number 19 in binary is 10011

You Try itConvert the following decimal numbers to binary123153

Addition on Binary

0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 10 (carry the 1)

1101 11010

+1001 +10011

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 00000011Try adding the binary numbers using a fixed size of 8 bits: 11011001+10001011

Internal and External Representation of Data

Real WorldIntegers: 34Signed Integers: -156Decimal Numbers:-23.431Text: HelloMusic: Hey JudePictures:

√

Signed Integers

-134

Sign/Magnitude Notation 110000110

magnitude

Sign0 = positive1 = negative

Not frequently used on computers•2 numbers for zero•Not easy to add/subtract

Signed Integers

-134

Two’s Complement Notation (for fixed size window 16)

1. Calculate the magnitude in binary0000000010000110

2. Flip the bits1111111101111001

3. Add one1111111101111010You Try it-129 -151

Internal and External Representation of Data

Real WorldIntegers: 34Signed Integers: -156Decimal Numbers:-23.431Text: HelloMusic: Hey JudePictures:

√√

Decimal Numbers5.75Write the 5 in binary and the 0.75 in binary5 – 1010.75 – 0.11Normalize the number, keeping track of Mantissa and

Exponent:±MxB±E

M – MantissaB – Base (we use base 2)E – Exponent

Used fixed size window (16 bits)First bit is signNext 9 bits are MantissaNext bit is signLast 5 bits are Exponent

You Try It: -8.25 11.5

Text

Fixed Size Window represents a characterASCII (8 bits) pg 141 in textUnicode (16 bits) represents 65,636 characters

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

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

Figure 4.5Digitization of an Analog Signal

(a) Sampling the Original Signal

(b) Recreating the Signal from the Sampled Values

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

Binary Representation of Sound and Images (continued)

Pictures

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

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

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

Binary Storage Devices

Figure 4.9Using Magnetic Cores to Represent Binary Values

Transistors

Solid-state switches; either permit or block current flow

A control input causes state change

Constructed from semiconductors

Binary Storage Devices (continued)

Figure 4.11Simplified Model of a Transistor