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CS 177 Week 2 Recitation Slides

Introduction

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Announcements

What Computers Understand?

Computers can only understand Encoding of numbers.

So what is the meaning of Encoding?

Computers are electronic devices that react to wires. Computer hardware produces (patterns of) voltages

(variations of electric current). If a wire has a voltage on it, we say that it encodes 1. If it has no voltage, we say 0.

How can we represent voltages?

Encoding is the activity of converting data or information into some symbol.

Computer understand just two symbols, 0 and 1.

0 and 1 are also numbers (in the binary number system). A binary number system gets its name from having just two digits, O and 1.

Encoding

Binary Number System

Represents numeric values using two symbols, 0 and 1 Also called Base-2 number system

To convert decimal numbers into binary, divide the decimal number repeatedly by 2 Remainder at each step becomes a digit of the binary number Repeat until result of further division becomes zero

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Decimal to Binary Conversion

To convert the decimal number 26 into binary,

In a computer, 26 is represented as 11010

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Binary to Decimal Conversion

Multiply successive digits of the binary number with increasing powers of 2

Add the products to get the

decimal number

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23 = 8 * 1 = 8 +22 = 4 * 1 = 4 +21 = 2 * 0 = 0 +20 = 1 * 1 = 1Interpreted as 13

Examples

Can you do this?

Example 1: Emoticons

What if you want to tell a friend your emotion by texting them on your mobile phone (without texting a long message)?

You can use emoticons… Emoticons are an encoding of emotions: :) I’m happy, I like it :( I’m unhappy, I dislike it :’( I’m crying and sad

You are using a combination of symbols (parenthesis, punctuation symbols), that you normally you use in writing, to represent your emotions.

Example 2: Character Codes

Now suppose that you want to encode the previous 3 symbols : ( ) using numbers…

You may use the ASCII code …

ASCII Table

Definitions

Bit: is the smallest unit of data in a computer that has a single binary value either 0 or 1.

Byte: is a unit of data that is eight binary digits long. How many bits are there in 5 bytes?

Questions

How many combinations can be represented in one bit? Two bits?

What about three bits and four bits?

So, Decoding is the activity of converting code into plain text.

Decoding

Statements

On starting Python, there is a Python prompt indicating that Python is ready to accept a command. These commands are called statements.

Different kinds of statements

>>> print("Hello, world“) Hello, world>>> print(2+3)5>>> print("2+3=", 2+3)2+3= 5>>>

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Simple Statements Assigning values

>>> a = 10

>>> b = 2

>>> c = 4

Arithmetic Operations

>>> x = a + b

>>> y = a – b

>>> p = a/b

>>> q = a/c

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Operator Precedence

Order of mathematical operations in an expression Python uses the same precedence as in Mathematics

Terms inside parentheses or brackets Exponents and Roots Multiplication and Division (Left to Right) Addition and Subtraction (Left to Right)

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Print Statements From previous example,

>>> print(x)

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>>> print("y =", y)

y = 8

>>> print("Sum of a and b :", a + b)

Sum of a and b : 12 Other examples,

>>> print("Hello, World!")

Hello, World!

>>> print("Hello", ",", "World!")

Hello , World! We will revisit the print() statement later

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Programming Tip

Use print() statements for debugging

>>> a = 2 + 3 * 6

>>> b = 10 - 2 * 3

>>> print(a/b)

5.0

Did we get the expected result?

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Print statements for debugging

Print statements allow us to observe the operator precedence

>>> a = 2 + 3 * 6

>>> print("a = ", a)

a = 20

>>> b = 10 - 2 * 3

>>> print("b = ", b)

b = 4

>>> print("Result = ", a/b)

Result = 5.0

Print statements allow us to observe various variables and the values they have during the course of the program

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Python Math Library

Provides access to mathematical functions Documentation – http://docs.python.org/library/math.html

math.pow(x, y) - Return x raised to the power y. math.sqrt(x) - Return the square root of x. math.factorial(x) - Return x factorial. math.ceil(x) - Return the ceiling of x. math.floor(x) - Return the floor of x.

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>>> import math

>>> a = math.factorial(6)

>>> print(a)

720

>>> b = math.sqrt(123)

>>> print(b)

11.0905365064

>>> c = math.floor(5.9)

>>> print(c)

5

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Examples

>>> x = math.factorial(4) * math.pow(2,3)

>>> print(x)

192.0

>>> y = 5.5

>>> z = math.floor(y) * math.ceil(y)

>>> print(z)

30

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Examples