Test Session Chapter 2 Number Systems (9th Computer Science and Entrepreneurship)

Multiple Choice Questions 10×1=10

1 How many bytes are used to store a typical integer?

A 1 byte

B 2 bytes

C 4 bytes

D 8 bytes

2 Convert the binary number 1011 to decimal:

A 11

B 13

C 9

D 15

3 Which step is part of converting decimal to binary?

Hint: Think about the repeated division method for decimal to binary conversion

A Divide by 8

B Multiply by 2

C Record remainder

D None of these

4 What is the minimum value of a 1-byte signed integer?

A –127

B –128

C 0

D –255

5 What is the binary representation of -6 in 8-bit two’s complement?

Two’s Complement: Invert bits and add 1

A 11111010

B 11111011

C 00000110

D 10000110

6 Which binary operation uses the rule 1 + 1 = 10?

A Addition

B Subtraction

C Multiplication

D Division

7 What does the ASCII code for the letter “P” represent in decimal?

A 80

B 112

C 65

D 97

8 How many bits are used in ASCII?

A 7

B 8

C 16

D 32

9 Which encoding scheme uses 4 bytes for all characters?

A UTF-8

B UTF-16

C UTF-32

D ASCII

10 What is the binary representation of the ASCII code for “A” (U+0041)?

01000001

A 01000001

B 01100001

C 00110001

D 01101000

Short Answer Questions 10×2=20

I How does Unicode handle characters from different languages?

ii Convert decimal 45 to octal.

Method: Divide by 8 repeatedly and record remainders in reverse order

iii What is the decimal value of binary 11100101?

Binary: 11100101
Decimal: 229

iv Convert 15 (decimal) to binary and octal.

v What is the range of a 2-byte signed integer?

vi How is overflow handled in binary addition?

vii How many partial products are generated in multiplying 101 by 11?

viii What is the ASCII code for the uppercase letter “K”?

ix Convert the ASCII code 105 to its corresponding character.

x What is the Unicode code point for the Urdu letter “-_”?

Detailed Answer Questions (Answer any 2) 2×5=10

1 Explain the process of converting decimal integers to its binary representation and vice versa. Include examples of both positive and negative integers.

Key Steps:
1. Positive numbers: Repeated division by 2, record remainders in reverse order
2. Negative numbers: Two’s complement method
3. Binary to decimal: Multiply each bit by 2^position and sum

2 Solve the following:
(a) \( 110_{2} – 010_{2} \)
(b) \( 101_{2} – 001_{2} \)
(c) \( 100_{2} – 011_{2} \)
(d) \( 111_{2} – 100_{2} \)

Remember: Binary subtraction uses borrow method or two’s complement addition

3 Explain the difference between 01111111 and 11111111 in 8-bit signed integer.

Consider: Sign bit (MSB), Two’s complement representation, Maximum and minimum values