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

Answer: Option 3

Explanation: 

Step 1: first we convert 147 to the Binary number system.

(147)10 = (10010011)2

Step 2: Now we group 4 bits to convert the Hexadecimal number system.

1001 0011

≡ (93)16

Convert binary to decimal :-

• For binary number with n digits:
• dn-1 ... d3 d2 d1 d0
• The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
• decimal = d0×20 + d1×21 + d2×22 + ...

Calculation:

Decimal equivalent of binary number 1001110 :-
=  1 × 2⁶ + 0 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 1 x 21 + 0 x 20

​= 64 + 0 + 0 + 8 + 4 + 2 + 0 = 78​

Binary to decimal conversion →

(129)₁₀ = (10000001)₂

0.25 → 0.25 × 2 = 0.5

0.5 × 2 = 1

(0.25)₁₀ = (.01)₂

(129.25)₁₀ = (10000001.01)₂

Answer: Option 2

Explanation:

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

So Octal Equivalent: 1353

Important Points

Binary to Octal code

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.

• 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

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.

Answer: Option 2

Explanation:

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

So Octal Equivalent: 1353

Important Points

Binary to Octal code

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

Mistake PointsThe question is asking for the 12^th 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'.

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:

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

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

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

Number System

The octal number system is represented by base 8.

The number system is a way to represent or express numbers. You have heard of various types of number systems such as the whole numbers and the real numbers. But in the context of computers, we define other types of number systems. They are: