Number Representation and Arithmetic: Master the Basics of Computer Arithmetic

Question 1

Which of the following is a valid binary representation of the decimal number 13?

Accepted Answer

1101

Answer

1011

Answer

1111

Answer

1100

Question 2

Which algorithm is employed for binary number multiplication?

Accepted Answer

Booth's algorithm

Answer

Dijkstra's algorithm

Answer

Bubble sort algorithm

Answer

Knuth-Morris-Pratt algorithm

Question 3

What is the base of the octal number system?

Accepted Answer

8

Answer

2

Answer

10

Answer

16

Question 4

Convert the decimal number 15 to its binary representation.

Accepted Answer

1001

Answer

1111

Answer

1101

Answer

1011

Question 5

What is the IEEE standard for single-precision floating-point numbers?

Accepted Answer

IEEE 754

Answer

IEEE 802.11

Answer

IEEE 1394

Answer

IEEE 608

Question 6

Select the operation that is not commonly performed in computer architecture.

Accepted Answer

Exponentiation

Answer

Addition

Answer

Subtraction

Answer

Division

Question 7

Which algorithm is commonly used for performing long division in computer architecture?

Accepted Answer

Horner's Method

Answer

Divide and Conquer

Answer

Binary Search

Answer

Newton-Raphson Method

Question 8

What is the primary purpose of an accumulator in computer architecture?

Accepted Answer

Storing the result of arithmetic operations

Answer

Holding the current operand

Answer

Performing arithmetic operations

Answer

Directing data flow within the ALU

Question 9

What is the decimal equivalent of the binary number 11111111?

Accepted Answer

255

Answer

127

Answer

511

Answer

256

Question 10

What is the radix of the octal number system?

Accepted Answer

8

Answer

2

Answer

10

Answer

16

Question 11

Which of the following is not an advantage of using binary numbers in computers?

Accepted Answer

Human readability

Answer

Simplicity of representation

Answer

Efficiency in processing

Answer

Compatibility with digital circuits

Question 12

What is the purpose of the sign bit in a signed number representation?

Accepted Answer

To indicate the sign of the number

Answer

To indicate the magnitude of the number

Answer

To identify the number system used

Answer

To represent the fractional part of the number

Question 13

Which arithmetic operation cannot be directly performed by a computer's ALU?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 14

What is the role of the overflow flag in arithmetic operations?

Accepted Answer

To indicate an out-of-range result

Answer

To indicate an incorrect result

Answer

To store the result of the operation

Answer

To reset the ALU for the next operation

Question 15

In Booth's algorithm, which register stores the previous value of Q?

Accepted Answer

Previous Q register

Answer

Multiplier register

Answer

Multiplicand register

Answer

Result register

Question 16

Which number system utilizes a base of 16?

Accepted Answer

Hexadecimal

Answer

Binary

Answer

Octal

Answer

Decimal

Question 17

Which of the following is not a fundamental arithmetic operation applicable to binary numbers?

Accepted Answer

Exponentiation

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 18

What is an advantage of using floating-point representation?

Accepted Answer

Compactly representing very large or very small numbers

Answer

Precisely representing all numbers

Answer

Enabling high-performance arithmetic operations

Answer

Representing all real numbers accurately

Question 19

What is the function of the exponent field in floating-point representation?

Accepted Answer

Determining the magnitude of the represented number

Answer

Indicating the position of the decimal point

Answer

Storing the sign of the represented number

Answer

Storing the precision of the represented number

Question 20

What is the purpose of the carry flag in an arithmetic operation?

Accepted Answer

Indicating overflow in the result

Answer

Indicating a negative result

Answer

Indicating a valid result

Answer

Indicating correct operation execution

Question 21

How does the size of registers affect the performance of arithmetic operations in a computer system?

Accepted Answer

Larger registers generally improve performance.

Answer

Smaller registers always lead to better performance.

Answer

Register size has no impact on arithmetic operation performance.

Answer

Mixing large and small registers optimizes performance.

Question 22

Which of the following accurately compares the precision, range, and bias of IEEE 754 single-precision and double-precision floating-point formats?

Accepted Answer

Double-precision: higher precision, larger range, larger bias

Answer

Single-precision: higher precision, smaller range, smaller bias

Answer

Both formats have the same precision, range, and bias

Question 23

Which numbering system is NOT a positional number system?

Accepted Answer

Roman

Answer

Decimal

Answer

Binary

Answer

Hexadecimal

Question 24

In the IEEE 754 single-precision floating-point format, what is the exponent bias?

Accepted Answer

127

Answer

255

Answer

64

Answer

32

Question 25

Which of the following is the Booth's algorithm primarily used for?

Accepted Answer

Multiplying binary numbers

Answer

Dividing binary numbers

Answer

Adding binary numbers

Answer

Subtracting binary numbers

Question 26

What is the primary purpose of a carry-save adder?

Accepted Answer

Adding multiple binary numbers simultaneously

Answer

Subtracting multiple binary numbers simultaneously

Answer

Multiplying multiple binary numbers simultaneously

Answer

Dividing multiple binary numbers simultaneously

Question 27

What is the primary purpose of a parity bit?

Accepted Answer

To detect errors in data transmission

Answer

To correct errors in data transmission

Answer

To improve the speed of data transmission

Answer

To reduce the size of data transmission

Question 28

What is the purpose of a sign-magnitude representation?

Accepted Answer

To represent negative numbers

Answer

To represent fractional numbers

Answer

To represent large numbers

Answer

To represent complex numbers

Question 29

What is one of the key benefits of using floating-point representation?

Accepted Answer

Wider dynamic range

Answer

Higher precision

Answer

Simplified arithmetic operations

Answer

Reduced memory usage

Question 30

Which part of the IEEE 754 floating-point standard uses a bias?

Accepted Answer

Exponent

Answer

Mantissa

Answer

Sign bit

Answer

Hidden bit

Question 31

What is a fundamental difference between the Von Neumann and Harvard architectures?

Accepted Answer

Different memory organization

Answer

Separate data and instruction buses

Answer

Different instruction sets

Answer

Different clock speeds

Question 32

What is the main goal of using a pipeline in a computer system?

Accepted Answer

To improve performance by overlapping instruction execution

Answer

To reduce the number of clock cycles required for operations

Answer

To handle interrupts

Answer

To store temporary data

Question 33

What is the primary purpose of a virtual memory system?

Accepted Answer

To extend the physical memory by using a portion of the storage device

Answer

To improve performance by reducing the number of page faults

Answer

To provide security by isolating processes' memory spaces

Answer

To handle memory allocation and deallocation

Question 34

In a 16-bit signed 2's complement representation, what is the largest negative number that can be represented?

Accepted Answer

0x8000

Answer

0x8001

Answer

0xFFFF

Answer

0x7FFF

Question 35

Convert the hexadecimal number 0xAB to its octal equivalent.

Accepted Answer

153

Answer

123

Answer

253

Answer

173

Question 36

What is the primary purpose of Booth's algorithm?

Accepted Answer

Multiplication of signed numbers

Answer

Division of unsigned numbers

Answer

Addition of floating-point numbers

Answer

Conversion between binary and decimal

Question 37

What does the overflow flag indicate in a subtraction operation?

Accepted Answer

The result is too large to be represented in the given bit width.

Answer

The result is negative.

Answer

The operands have different signs.

Answer

The result is zero.

Question 38

Which of the following is NOT an advantage of the floating-point representation?

Accepted Answer

Reduced storage space

Answer

Higher precision

Answer

Wider dynamic range

Answer

Improved accuracy

Question 39

What is the purpose of the normalization step in floating-point arithmetic?

Accepted Answer

To adjust the exponent within a specific range.

Answer

To ensure the mantissa is less than 1.

Answer

To increase the precision of the result.

Answer

To simplify the arithmetic operations.

Question 40

Subtract the signed 4-bit binary number A = 1010 from B = 0111 using 2's complement representation. What is the result?

Accepted Answer

-1

Answer

1

Answer

5

Answer

10

Question 41

Which algorithm is used for floating-point addition?

Accepted Answer

IEEE 754 standard

Answer

Brent-Kung adder

Answer

Booth's algorithm

Answer

Radix-4 Booth algorithm

Question 42

What is the purpose of a carry-lookahead adder?

Accepted Answer

To reduce the delay in propagating carry signals.

Answer

To increase the accuracy of addition.

Answer

To perform subtraction more efficiently.

Answer

To handle floating-point numbers.

Question 43

Which is a type of floating-point representation?

Accepted Answer

IEEE 754 standard

Answer

2's complement representation

Answer

Fixed-point representation

Answer

Gray code

Question 44

What is the key difference between signed and unsigned numbers?

Accepted Answer

Signed numbers can represent both positive and negative values, while unsigned numbers can only represent positive values and zero.

Answer

Unsigned numbers can represent both positive and negative values, while signed numbers can only represent positive values and zero.

Question 45

When representing the decimal number -5 in 8-bit two's complement, which of the following binary values is **incorrect**?

Accepted Answer

11111001

Answer

11111101

Answer

11111011

Answer

10000101

Question 46

What is the largest positive number that can be represented using a 16-bit unsigned integer?

Accepted Answer

65535

Answer

32768

Answer

32767

Answer

65536

Question 47

What is the primary advantage of using floating-point representation over fixed-point representation?

Accepted Answer

Ability to represent a wider range of numbers, including very small and very large values.

Answer

Faster arithmetic operations for all types of calculations.

Answer

More precise representation for all numbers.

Question 48

Which of the following accurately describes the characteristic of overflow in two's complement arithmetic?

Accepted Answer

The result of an operation exceeds the representable range of the fixed-width format, leading to an incorrect result.

Answer

The result of the operation is always negative.

Answer

The result of the operation is always zero.

Question 49

In two's complement representation, what is the purpose of the sign bit?

Accepted Answer

The sign bit indicates whether the number is positive or negative.

Answer

The sign bit represents the magnitude of the number.

Answer

The sign bit represents the radix of the number system.

Question 50

When a processor performs division on two binary numbers, what specific error condition arises if the divisor is zero?

Accepted Answer

Division by zero error

Answer

Overflow error

Answer

Underflow error