CS304PC:Computer Organization and Architecture

1. CS304PC:Computer Organization
and Architecture (R18 II(I sem))
Department of computer science and engineering
(AI/ML)
Session 16
by
Asst.Prof.M.Gokilavani
VITS
1/31/2023 Department of CSE (AI/ML) 1

2. TEXTBOOK:
• 1. Computer System Architecture – M. Moris Mano, Third Edition,
Pearson/PHI.
REFERENCES:
• Computer Organization – Car Hamacher, Zvonks Vranesic, Safea
Zaky, Vth Edition, McGraw Hill.
• Computer Organization and Architecture – William Stallings Sixth
Edition, Pearson/PHI.
• Structured Computer Organization – Andrew S. Tanenbaum, 4th
Edition, PHI/Pearson.
1/31/2023 Department of CSE (AI/ML) 2

3. Unit III
Data Representation: Data types ,Complements, fixed point
Representations, Floating point representation.
Computer Arithmetic: Addition and subtraction,
multiplication Algorithms, Division Algorithms, Floating-point
Arithmetic operations, Decimal Arithmetic unit, Decimal
Arithmetic operations.
1/31/2023 Department of CSE (AI/ML) 3

4. Topics covered in session 16
1/31/2023 Department of CSE (AI/ML) 4
• Data types
• Complements
• Fixed point Representations
• Floating point representations

5. Data types
• Registers contain either data or control information
• Control information is a bit or group of bits used to specify the sequence of
command signals needed for data manipulation
• Data are numbers and other binary-coded information that are operated on
• Possible data types in registers:
o Numbers used in computations
o Letters of the alphabet used in data processing
o Other discrete symbols used for specific purposes
• All types of data, except binary numbers, are represented in binary-coded
form.
• This is because register are made up of Flip-Flops and Flip-Flops are two-
state devices that can store only 1’s and 0’s.
1/31/2023 Department of CSE (AI/ML) 5

6. Number systems
• A number system of base, or radix, r is a system that uses distinct symbols for r digits.
Numbers are represented by a string of digit symbols .
• Conversion of Binary to decimal: The string of digits 101101 in the binary number
system represents the quantity
1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 45
(101101)2 = (45)10
• We will also use the octal (radix 8) and hexadecimal (radix 16) number systems
Conversion of Octal to decimal : (736.4)8
7 x 82 + 3 x 81 + 6 x 80 + 4 x 8-1 = (478.5)10
Conversion of hexadecimal to octal: (F3)16
F x 161 + 3 x 160 = (243)10
1/31/2023 Department of CSE (AI/ML) 6

7. Recap of Number System
• Convert Decimal equivalent 98 into binary Equivalent.
• Convert the following binary numbers to decimal.
i. 101110
ii. 1110101
iii. 110110100
1/31/2023 Department of CSE (AI/ML) 7

8. Convert Decimal equivalent 98 into binary
Equivalent .
1/31/2023 Department of CSE (AI/ML) 8

9. • Convert the following binary numbers to decimal.
i. 101110
ii. 1110101
iii. 110110100
1/31/2023 Department of CSE (AI/ML) 9

10. • Conversion from decimal to radix r system is carried out by separating
the number into its integer and fraction parts and converting each part
separately
1/31/2023 Department of CSE (AI/ML) 10

11. Convert decimal number 98.46 into binary
numbers.
1/31/2023 Department of CSE (AI/ML) 11

12. Octal to Hexadecimal number
• Each octal digit corresponds to three binary digits
• Each hexadecimal digit corresponds to four binary digits
• Rather than specifying numbers in binary form, refer to them in octal or
hexadecimal and reduce the number of digits by 1/3 or ¼, respectively.
1/31/2023 Department of CSE (AI/ML) 12

13. 1/31/2023 Department of CSE (AI/ML) 13

14. 1/31/2023 Department of CSE (AI/ML) 14

15. Question
Convert the following decimal number to the
bases indicated
a. 7562 to octal
b.1938 to hexadecimal
c. 175 to binary
1/31/2023 Department of CSE (AI/ML) 15

16. Decimal representation
• Numerous different codes can be obtained by arranging four
bits in 10 distinct combinations.
• Binary-coded decimal (BCD) is a class of binary encodings
of decimal numbers where each digit is represented by a fixed
number of bits, usually four or eight.
• Sometimes, special bit patterns are used for a sign or other
indications (E.g: error or overflow). This particular code is
called binary coded decimal and commonly know as BCD.
1/31/2023 Department of CSE (AI/ML) 16

17. 1/31/2023 Department of CSE (AI/ML) 17

18. BCD
• A binary code is a group of n bits that assume up to 2n distinct
combinations
• A four bit code is necessary to represent the ten decimal digits – 6 are
unused
• The most popular decimal code is called binary-coded decimal (BCD)
• BCD is different from converting a decimal number to binary
• For example 99, when converted to binary, is 1100011
• 99 when represented in BCD is 1001 1001
1/31/2023 Department of CSE (AI/ML) 18

19. Question
1. Convert Decimal Equivalent 278 to BCD
number.
1/31/2023 Department of CSE (AI/ML) 19

20. 1/31/2023 Department of CSE (AI/ML) 20

21. Question
1.
2.
1/31/2023 Department of CSE (AI/ML) 21

22. ASCII
• The standard alphanumeric binary code is ASCII
• This uses seven bits to code 128 characters
• Binary codes are required since registers can hold binary information
only
1/31/2023 Department of CSE (AI/ML) 22

23. 1/31/2023 Department of CSE (AI/ML) 23

24. Question
1.
1/31/2023 Department of CSE (AI/ML) 24

25. Topics to be covered in next session 17
• Complements
1/31/2023 Department of CSE (AI/ML) 25
Thank you!!!