Number System MCQ Quiz - Objective Question with Answer for Number System - Download Free PDF

Last updated on May 30, 2025

Latest Number System MCQ Objective Questions

Number System Question 1:

What is the 2's complement of the binary number 101110?

  1. 010011
  2. 010010
  3. 110001
  4. 010001

Answer (Detailed Solution Below)

Option 2 : 010010

Number System Question 1 Detailed Solution

The correct answer is 010010

Key Points

  • The two's complement of a binary number is found by inverting all of the bits, known as the one's complement, and then adding 1.
  • The binary number 101110's inverted binary number (one's complement) would be 010001.
  • Next, you add 1 to the inverted binary number:

         010001

                 +1

         010010

Therefore, the 2's complement of the binary number 101110 is 010010.

Number System Question 2:

Which of the following is the correct octal representation of the hexadecimal number 1A3?

  1. 346
  2. 124
  3. 634
  4. 643

Answer (Detailed Solution Below)

Option 4 : 643

Number System Question 2 Detailed Solution

Explanation:

Hexadecimal to Octal Conversion

Definition: Hexadecimal and octal are both positional numeral systems, widely used in computing and digital electronics. Hexadecimal (base-16) uses sixteen symbols, 0-9 and A-F, to represent values, while octal (base-8) uses eight symbols, 0-7.

To convert a hexadecimal number to its octal equivalent, it is often easiest to first convert it to binary (base-2), and then from binary to octal. This method works because both octal and hexadecimal are powers of 2 (octal is 23 and hexadecimal is 24).

Step-by-Step Solution:

Given hexadecimal number: 1A3

1. Convert Hexadecimal to Binary:

Each hexadecimal digit can be represented by a 4-bit binary number:

  • 1 (Hex) = 0001 (Binary)
  • A (Hex) = 1010 (Binary)
  • 3 (Hex) = 0011 (Binary)

So, the hexadecimal number 1A3 can be written in binary as: 0001 1010 0011

2. Group Binary Digits into Sets of Three:

Since octal is base-8 and each octal digit corresponds to 3 binary digits, we group the binary digits in sets of three, starting from the right:

  • 0001 1010 0011 (Binary)
  • 000 110 100 011 (Binary, grouped in sets of three)

3. Convert Binary Sets to Octal:

Each group of three binary digits can be converted directly to its octal equivalent:

  • 000 (Binary) = 0 (Octal)
  • 110 (Binary) = 6 (Octal)
  • 100 (Binary) = 4 (Octal)
  • 011 (Binary) = 3 (Octal)

So, the binary number 000 110 100 011 can be written in octal as: 0643

Hence, the correct octal representation of the hexadecimal number 1A3 is 643.

Important Information:

To analyze other options, let's convert the hexadecimal number 1A3 using the same method:

  • Option 1: 346
    • 346 (Octal) in binary: 011 100 110
    • Groups: 011 100 110 (Binary) = 3 4 6 (Octal)
    • Binary to Hexadecimal: 011100110 (Binary) = 1C6 (Hex)
    • 1C6 ≠ 1A3
  • Option 2: 124
    • 124 (Octal) in binary: 001 010 100
    • Groups: 001 010 100 (Binary) = 1 2 4 (Octal)
    • Binary to Hexadecimal: 001010100 (Binary) = 54 (Hex)
    • 54 ≠ 1A3
  • Option 3: 634
    • 634 (Octal) in binary: 110 011 100
    • Groups: 110 011 100 (Binary) = 6 3 4 (Octal)
    • Binary to Hexadecimal: 110011100 (Binary) = 19C (Hex)
    • 19C ≠ 1A3

Therefore, the correct option is confirmed as option 4: 643.

Number System Question 3:

What happens to the carry-out bit when subtracting two n-bit numbers using 2's complement and the result is positive?

  1. The carry-out bit indicates an overflow
  2. The carry-out bit is added to the result
  3. The carry-out bit is inverted
  4. The carry-out bit is ignored

Answer (Detailed Solution Below)

Option 4 : The carry-out bit is ignored

Number System Question 3 Detailed Solution

Explanation:

Correct Option - The carry-out bit is ignored

When subtracting two n-bit numbers using 2's complement and the result is positive, the carry-out bit does not have a significant role in determining the outcome of the subtraction. The carry-out bit is essentially ignored in this scenario. This is due to the way 2's complement arithmetic handles overflow and underflow conditions.

Understanding 2's Complement Representation:

2's complement representation is a method used to encode signed integers in binary. In this representation, positive numbers are represented as usual in binary, while negative numbers are represented by taking the binary representation of the absolute value, inverting all the bits (creating the 1's complement), and then adding one to the least significant bit.

For example:

  • +5 in 4-bit binary: 0101
  • -5 in 4-bit 2's complement: 1011 (1's complement of 0101 is 1010, add 1 to get 1011)

 

Subtraction Using 2's Complement:

When performing subtraction using 2's complement, we add the 2's complement of the number to be subtracted. For instance, to compute A - B, we actually calculate A + (-B). The process involves the following steps:

  • Compute the 2's complement of B (which gives -B).
  • Add this value to A.
  • Check the result for any overflow or underflow conditions.

 

Carry-out Bit:

The carry-out bit is a bit that is carried out of the most significant bit position when performing binary addition or subtraction. In the context of 2's complement subtraction, the carry-out bit can indicate whether an overflow has occurred, but it does not affect the correctness of the result itself. If the result of the subtraction is positive, it means that the result fits within the range of representable values for the given bit-width, and thus, the carry-out bit is ignored.

Analysis of Other Options:

Option 1: The carry-out bit indicates an overflow

This option is incorrect because the carry-out bit alone does not indicate an overflow in the context of 2's complement arithmetic. Overflow is determined by examining the sign bits of the operands and the result, not just the carry-out bit. For example, if adding two positive numbers results in a negative number, or adding two negative numbers results in a positive number, an overflow has occurred.

Option 2: The carry-out bit is added to the result

This option is incorrect because the carry-out bit is not added to the result in 2's complement arithmetic. The carry-out bit is discarded, and the result is taken as-is unless overflow has occurred, which needs to be handled separately.

Option 3: The carry-out bit is inverted

This option is incorrect because inverting the carry-out bit has no meaningful impact on the result of the 2's complement subtraction. The carry-out bit does not affect the final result and is simply ignored if the result is within the valid range.

Option 4: The carry-out bit is ignored

This is the correct option, as explained above. The carry-out bit does not affect the result of the subtraction if the result is positive and within the representable range of the bit-width.

Important Information:

Understanding the carry-out bit and its role in binary arithmetic is crucial for anyone working with digital systems and computer architecture. The carry-out bit can indicate different conditions depending on the context, such as overflow or borrow in subtraction, but in the case of 2's complement arithmetic, it is ignored if the result is positive and valid.

Additionally, understanding the principles of 2's complement representation and arithmetic is foundational for designing and analyzing algorithms that involve signed integer calculations. This knowledge is essential for fields like embedded systems, computer engineering, and digital signal processing, where precise manipulation of binary data is required.

Number System Question 4:

EBCDIC coding scheme uses ______ bits to code different characters.

  1. 4
  2. 8
  3. 16
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 2 : 8

Number System Question 4 Detailed Solution

Extended Binary Coded Decimal Interchange Code is an eight-bit character encoding used mainly on IBM mainframe and IBM midrange computer operating systems.

EBCDIC was devised in 1963 and 1964 by IBM. It is an eight-bit character encoding, developed separately from the seven-bit ASCII encoding scheme.

Number System Question 5:

Match the LIST-I with LIST-II

LIST - I

Boolean Algebra Law

LIST - II

Axioms

A.

Absorption Law

I.

a + 1 = 1

B.

Bounded Law

II.

a + 0 = a

C.

Identity Law

III.

a * (b + c) = (a * b) + (a * c)

D.

Distributive Law

IV.

a + (a * b) = a


Choose the correct answer from the options given below:

  1. A - IV, B - I, C - II, D - III 
  2. A - IV, B - III, C - I, D - II 
  3. A - III, B - IV, C - II, D - I 
  4. A - II, B - III, C - IV, D - I

Answer (Detailed Solution Below)

Option 1 : A - IV, B - I, C - II, D - III 

Number System Question 5 Detailed Solution

The correct answer is Option 1.

Key Points

  • The correct matching of Boolean Algebra Laws with their corresponding Axioms is as follows:
    • Absorption Law: a + (a * b) = a
    • Bounded Law: a + 1 = 1
    • Identity Law: a + 0 = a
    • Distributive Law: a * (b + c) = (a * b) + (a * c)
  • Based on this, the correct matching is:
    • A - IV (Absorption Law - a + (a * b) = a)
    • B - I (Bounded Law - a + 1 = 1)
    • C - II (Identity Law - a + 0 = a)
    • D - III (Distributive Law - a * (b + c) = (a * b) + (a * c))

Additional Information

  • Understanding Boolean Algebra is essential in digital electronics and computer science for designing and analyzing digital circuits.
  • Boolean Algebra allows for the simplification of logic expressions, making it easier to implement and optimize digital systems.
  • These fundamental laws and axioms provide the foundation for more complex theorems and applications in Boolean logic and digital design.

Top Number System MCQ Objective Questions

Binary number 101110110 is equal to decimal number _______.

  1. 468
  2. 412
  3. 374
  4. 326

Answer (Detailed Solution Below)

Option 3 : 374

Number System Question 6 Detailed Solution

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  • The correct answer is option 3, i.e., 374.
  • Binary number 101110110 is equal to decimal number 374.
  • Following method can be used to convert Binary number to Decimal number:
  1. (101110110)2 = (1 x 28) + (0 x 27) + (1 x 26) + (1 x 25) + (1 x 24) + (0 x 23) + (1 x 22) + (1 x 21) + (0 x 20)
  2. (101110110)2 = 256 + 0 + 64 + 32 + 16 + 0 + 4 + 2 + 0
  3. (101110110)2 = 374

One megabyte In base 2 (binary) Is equivalent to             .

  1. 103 bytes
  2. 104 bytes
  3. 210 bytes
  4. 220 bytes

Answer (Detailed Solution Below)

Option 4 : 220 bytes

Number System Question 7 Detailed Solution

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The correct answer is 220 bytes.

Key Points

  • 1 Megabyte is equal to 1000000 bytes (decimal).
  • 1 MB = 106 B in base 10 (SI).
  • 1 Megabyte is equal to 1048576 bytes (binary).
  • 1 MB = 220 B in base 2.
  • Byte is the basic unit of digital information transmission and storage, used extensively in information technology, digital technology, and other related fields. It is one of the smallest units of memory in computer technology, as well as one of the most basic data measurement units in programming.
  • The earliest computers were made with the processor supporting 1 byte commands, because in 1 byte you can send 256 commands. 1 byte consists of 8 bits,
  • Megabyte (MB) is a unit of transferred or stored digital information, which is extensively used in information and computer technology.
  • In SI, one megabyte is equal to 1,000,000 bytes. At the same time, practically 1 megabyte is used as 220 B, which means 1,048,576 bytes.

625e5fa7f8c06b4efbb09cf9 16544040466351

The Octal equivalent of the binary number 1011101011 is:

  1. 7353
  2. 1353
  3. 5651
  4. 5657

Answer (Detailed Solution Below)

Option 2 : 1353

Number System Question 8 Detailed Solution

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Answer: Option 2

Explanation:

An octal Equivalent of a binary number is obtained by grouping 3 bits from right to left.

001 011 101 011
1 3 5 3


So Octal Equivalent: 1353

Important Points

Binary to Octal code

000

001

010

011

100

101

110

111

0

1

2

3

4

5

6

7

The number of 1s in the binary representation of (3 ⋆ 4096 + 15 ⋆ 256 + 5 ⋆ 16 + 3) are  

  1. 8
  2. 9
  3. 10
  4. 12

Answer (Detailed Solution Below)

Option 3 : 10

Number System Question 9 Detailed Solution

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Application:

Decimal value = (3 ⋆ 4096 + 15 ⋆ 256 + 5 ⋆ 16 + 3)

It can be written as:

(2 + 1) × 212 + (8 + 4 + 2 + 20) × 28 + (4 + 1) × 24  + (2 + 1) × 20

21 × 212 + 20 × 212 + (23 + 22 + 21 + 20) × 28 + (22 + 20) × 24 + (21 + 20) × 20

This can be written as:

213 + 212 + 211 + 210 + 29 × 28 + 26 + 24 + 21 + 20

The binary representation will be:

(11111101010011)2

The 12th digit in standard hexadecimal system is equal to:

  1. D
  2. B
  3. A
  4. C

Answer (Detailed Solution Below)

Option 2 : B

Number System Question 10 Detailed Solution

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Mistake Points
The question is asking for the 12th Digit in Hexadecimal representation, i.e. 0 will be the first digit, 1 will be the second, and so on.

The correct answer is (option 2) i.e. B

Explanation:

Digits in hexadecimal number systems are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Therefore, the total number of different digits in hexadecimal number systems is 16.

Hence 12th digit in the hexadecimal system is B. And it is equivalent to 11 for Decimal and 1011 for the Binary number system,

Important Points

  • Digits in decimal number systems are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Therefore, number of different digits in decimal number systems is 10.
  • Digits in Octal number systems are 0, 1, 2, 3, 4, 5, 6, 7. Therefore, number of different digits in octal number systems is 8.
  • Digits in binary number systems are 0, 1. Therefore, number of different digits in binary number systems is 2.
  • In the standard hexadecimal system, each digit can have 16 possible values, ranging from 0 to 9 and then A to F, representing the values 10 to 15.
  • To determine the 12th digit in the standard hexadecimal system, we need to convert the number 12 from decimal to hexadecimal.
  • 12 in decimal is equal to B in hexadecimal. Therefore, the 12th digit in the standard hexadecimal system is option 4) B.

The hexadecimal system is a number system with a base of 16. It is commonly used in computing and digital systems because it provides a convenient way to represent binary numbers. In hexadecimal, the digits range from 0 to 9, and then use the letters A to F to represent values 10 to 15.

Here's a breakdown of the digits leading up to the 12th position:

  • 1st digit: 0
  • 2nd digit: 1
  • 3rd digit: 2
  • 4th digit: 3
  • 5th digit: 4
  • 6th digit: 5
  • 7th digit: 6
  • 8th digit: 7
  • 9th digit: 8
  • 10th digit: 9
  • 11th digit: A
  • 12th digit: B

Therefore, the 12th digit in the standard hexadecimal system is 'B'.

Excess - 3 - code is also known as

  1. Weighted code
  2. Cyclic redundancy code
  3. Self-complementing code
  4. Algebraic code

Answer (Detailed Solution Below)

Option 3 : Self-complementing code

Number System Question 11 Detailed Solution

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Excess - 3 - code is also known as self-complementing code which means 1's complement of an excess - 3 number is the excess - 3 code for the 9's complement of the corresponding decimal number.

Example:

1  in binary is 0001

excess 3 code is 0001 + 0011 = 0100

1's complement of the above code is 1011 which is 11 

11 is excess 3 code for 8

and 9's complement of 1 is 8

26 June 1

Decimal

Excess – 3 code

Binary

Gray code

Octal

0

0011

0000

0000

000

1

0100

0001

0001

001

2

0101

0010

0011

010

3

0110

0011

0010

011

4

0111

0100

0110

100

5

1000

0101

0111

101

6

1001

0110

0101

110

7

1010

0111

0100

111

8

1011

1000

1100

001 000

The hexadecimal equivalent of the decimal number 4096 is ____.

  1. 1000
  2. F100
  3. F0
  4. 1F0

Answer (Detailed Solution Below)

Option 1 : 1000

Number System Question 12 Detailed Solution

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Concept:

  • To convert a decimal number system to hexadecimal, we follow the successive division approach i.e. we divide the decimal number by 16 and note down the remainder.
  • Each remainder is then expressed in hexadecimal.

 

Calculation:

F1 Neha Madhu 17.10.20 D3

So, The hexadecimal equivalent of decimal number 4096 is 1000. 

Find x = ?

If (356)8 = (x)16

  1. EA
  2. A8
  3. 7E
  4. EE

Answer (Detailed Solution Below)

Option 4 : EE

Number System Question 13 Detailed Solution

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The correct answer is option 4.

Concept:

Hexadecimal number system:

The hexadecimal number system is a kind of number system with a base value of 16 characters. It is also spelled 'hex' at times. Only 16 symbols are used to represent hexadecimal values. These are the values or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each number corresponds to a decimal value.

Octal Number System:

The Octal Number System has an eight-digit basis and employs numbers ranging from 0 to 7. When paired in pairs of three, octal numbers are commonly represented as binary numbers in the number system.

Explanation:

The given data,

If (356)8 = (x)16

Convert the octal number to binary and then convert it into Hexa decimal.

3= 011

5= 101

6= 110

(011 101 110)2= (0 1110 1110)2

1110= E

(0 E E)16

Hence the correct answer is EE.

Alternate Method The given data,

If (356)8 = (x)16

Convert the octal number to decimal and then convert it into Hexa decimal.

(356)8 =(3 x 82+ 5 x 81+6 x 80)10

(356)8 =(238)10

(356)8 =(238)10 =(EE)16

Which type of number system is represented by base 8?

  1. Decimal 
  2. Binary 
  3. Octal 
  4. hexadecimal 

Answer (Detailed Solution Below)

Option 3 : Octal 

Number System Question 14 Detailed Solution

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Number System

The octal number system is represented by base 8.

Number System

Base

Maximum no. of bits

Range

Binary

2

2

0-1

Decimal

10

4

0-9

Octal

8

3

0-7

Hexadecimal

16

4

0-15

What is the 1's complement of 0000 1111 0010 1101 number?

  1. 1111 1100 1010 1100
  2. 1111 0000 1101 0010
  3. 1111 0000 0010 1101
  4. 1001 0010 1010 1100

Answer (Detailed Solution Below)

Option 2 : 1111 0000 1101 0010

Number System Question 15 Detailed Solution

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The correct answer is 1111 0000 1101 0010

Key Points

A binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). 

Calculation

Given number = 0000 1111 0010 1101

1's complement is obtained by changing all 0's to 1's and all 1's to 0's. 

Hence, 1's complement = Invert bits = 1111 0000 1101 0010

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