1. CS1001 Programming Fundamentals 3(3-0) Lecture 2
Binary Arithmetic and Over View of Software Development
Lecture: Narong Wesnarat

2. Binary Arithmetic
The individual digits of a binary number are referred to as bits
Each bit represents a power of two
Examples
= 0 • • • • • 20 = 11
= 0 • • • • • 20 = 2
00010
01101
Binary
addition 2
+ 11 13
Equivalent
decimal addition

3. Binary Arithmetic 0101 Binary Equivalent decimal multiplication
× 0011
0000 5
× 3 15

4. Two’s Complement
Convention for handling signed numbers in binary representation
The leading bit is a sign bit
Binary number with leading 0 is positive
Binary number with leading 1 is negative
Magnitude of positive numbers is just the binary representation
Magnitude of negative numbers is found by performing the two’s complement
Complement the bits
Replace all the 1's with 0's, and all the 0's with 1's
Add one to the complemented number
Carry in most significant bit position is thrown away when performing arithmetic

5. Two's Complement Example
Performing two's complement on the decimal 7 to get -7
Using a five-bit representation
7 = Convert to binary
Complement the bits
Add 1 to the complement
Is -7 in two's complement (Answer)

6. Two's Complement Arithmetic
Computing using a two's complement representation with five-bit numbers
In base 10 (Decimal System)
= 8 + (-7) = 1
Using Two’s Complement Arithmetic
Two's complement of 8
Two's complement of -7
Add 8 and -7
100001
Is the five-bit result
Throw away the high-order carry as we are using a five bit representation

7. Integer Constants
Integer constants are positive or negative whole numbers
Integer constant forms
Decimal (base 10)
Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Octal (base 8)
Digits 0, 1, 2, 3, 4, 5, 6, 7
Hexadecimal (base 16)
Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a , b, c, d, e, f
Consider
31 oct and 25 dec

8. Hexadecimal Constants
Letters represent the hex digits
a or A d or D - 13
b or B e or E - 14
c or C f or F - 15
Examples (in C language)
0x2C
0XAC12EL
The type of the constant depends on its size, unless the type specifier is used

9. 1.4 The Software Development Method (Hanly’s Text book)
Specify the problem requirements
Analyse the problem
Design the algorithm to solve the problem
Implement the algorithm
Test and verify the completed program
Maintain and update the program

10. 1.5 Applying the software Development Method
CASE STUDY Converting Miles to Kilometers
Problem
Convert distances from miles into kilometers.
Analysis
DATA REQUIREMENTS
Problem Inputs: miles /* the distance in miles */
Problem Output: kms /*the distance in kilomieters*/
Relevant Formula: 1 mile = kilometers

11. 1.5 Applying the software Development Method
Design
ALGORITHM
Get the distance in miles
Convert the distance to kilometers
Display the distance in kilometers
Altorithm with Refinements
2.1 The distance in kilometers is times the distance in miles

12. 1.5 Applying the software Development Method
IMPLEMENTATION
Figure Miles-to-Kilometers Conversion Program

13. Basic Software Design Tools
Simple program design tools
Flowchart
Pseuso-code
Visit a link for complete Flowchart Symbols at the instructor’s Web site

14. Flowchart Analyzing the Flowchart (Checking your algorithm)
Suppose we Enter N = 3, The process of Printing 1 -3 will be:
Step 1 2 3 4 5 6 N I
Printed on Paper 12
123
Decision No
Yes
Stop

15. Introduction Pseudo-Code
Pseudo-code is a way to express an
algorithm ...
... using a structured form of language ...
... that is (hopefully) unambiguous ...
... and resembles a programming language.
There are no rules ...
... but there might be standards.

16. Introduction Pseudo-Code
The Sequence (instructions in series)
some statement
another statement
If-Then-Else statement (decision)
If some condition is TRUE
Then some statements
Else another statement
Else (maybe) no statement

17. Introduction Pseudo-Code
While-Do statement (loop)
WHILE the condition is TRUE do
some statement
another statement
ENDWHILE or WEND
Repeat-Until statement (loop)
REPEAT
UNTIL the condition is TRUE

18. Introduction Pseudo-Code
Case statement (multiple decision)
CASE condition is :
value-1 : statement
another statement
value-2: statement
value-3: statement
ENDCASE

19. Introduction Pseudo-Code
(more) Keywords:
Read , Write used for input description
(also: Input, Ouput)
true , false used to state a logical result
Add , Subtract
Multiply , Divide used for calculations
AND , OR , NOT used for combined Conditions
Hints and Tips:
In principal there are 3 Pseudocode structures:
Sequence, Loop and Decision.
With those three, you can describe any Algorithm (solution to
a problem), using Pseudo-code.

20. Introduction Pseudo-Code
Some examples
If-Then_Else (decision)
Problem: Read one number and check if it is positive!
Pseudo-Code:
Read number
If number > zero
Then Write “Number is Positive!”
Else Write “Number is Negative!”
This simple algorithm will read one Number as Input (from the keyboard if nothing else is specified), will check if that
Number is Positive or not and will print the result (on the
Monitor, if nothing else is specified)

21. Introduction Pseudo-Code
The solution above will not solve all cases though! That’s
because the number could also be zero, and then you cannot tell whether it is positive or negative! So we improve our solution to the problem by changing the PSEUDOCODE to:
Read number
If number > zero
Then Write “Number is Positive!”
Else If number = zero
Then Write “Number is Zero!”
Else Write “Number is Negative!”

22. Introduction Pseudo-Code
Suppose we would like to use the CASE-statement here, then it would look like following:
Read Number
CASE Number is :
> zero : Write “Number is Positive!”
= Zero : Write “Number is zero!”
< Zero : Write “Number is Negative!”
ENDCASE

23.   Structured Flow chart Flowchart should be structured
These two flowchart gives the same result but the right one is better.
Flowchart should be structured
easier to implement in high level language
easier to find errors
Use only standard structures
sequence
IF… THEN … ELSE …
REPEAT…. UNTIL …..
WHILE …. DO …..
…..
WEND  

24. Flowchart & Pseudo-code comparison
Read N
I = 0
REPEAT
Print I
I = I + 1
UNTIL I = N