Download - CPSC 171 Introduction to Computer Science
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