CPSC 171 Introduction to Computer Science Binary

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 2 nd in class

Example Representation 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 …

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

Integer Representation We use a base 10 number system (Decimal) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 2,359 tens hundreds thousands ones Computers use a base 2 number system (Binary) 0,

Conversion from Binary to Decimal 1x2 5 +1x2 4 +0x2 3 +1x2 2 +0x2 1 +1x2 0 =53 You Try it: What are the following binary numbers in decimal?

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

Addition on Binary = = = = 10 (carry the 1)

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 Try adding the binary numbers using a fixed size of 8 bits:

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

Signed Integers -134 Sign/Magnitude Notation magnitude Sign 0 = positive 1 = 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 binary Flip the bits Add one You Try it

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

Decimal Numbers 5.75 Write the 5 in binary and the 0.75 in binary 5 – – 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:

Text Fixed Size Window represents a character ASCII (8 bits)pg 141 in text Unicode (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 4.5 Digitization 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 (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 4.9 Using 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 4.11 Simplified Model of a Transistor