Hexadecimal MCQ Quiz - Objective Question with Answer for Hexadecimal - Download Free PDF

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.

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 160

Key Points

The hexadecimal number system, or base 16, uses 16 digits: 0-9 and A-F, where A represents 10, B is 11, up to F which represents 15.

The hexadecimal number A0 can be converted to decimal by multiplying each digit by 16 raised to its position from right (starting from 0).

So, converting the hexadecimal value 'A0' to a decimal value would look like this:

    A = 10 

    A0 = 100

    = 10 * (16¹) + 0 * (16⁰)

    = 160 + 0 = 160

So, the correct answer is: 160

The correct answer is 160

Key Points

The hexadecimal number system, or base 16, uses 16 digits: 0-9 and A-F, where A represents 10, B is 11, up to F which represents 15.

The hexadecimal number A0 can be converted to decimal by multiplying each digit by 16 raised to its position from right (starting from 0).

So, converting the hexadecimal value 'A0' to a decimal value would look like this:

    A = 10 

    A0 = 100

    = 10 * (16¹) + 0 * (16⁰)

    = 160 + 0 = 160

So, the correct answer is: 160

The correct answer is 160

Key Points

The hexadecimal number system, or base 16, uses 16 digits: 0-9 and A-F, where A represents 10, B is 11, up to F which represents 15.

The hexadecimal number A0 can be converted to decimal by multiplying each digit by 16 raised to its position from right (starting from 0).

So, converting the hexadecimal value 'A0' to a decimal value would look like this:

    A = 10 

    A0 = 100

    = 10 * (16¹) + 0 * (16⁰)

    = 160 + 0 = 160

So, the correct answer is: 160

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. 

Concept:

Step 1: Conversion: Octal to decimal

Step 2: Conversion: decimal to Hexadecimal

Calculation:

Step 1:

Conversion: Octal to decimal

(65)8 = 6 × 8 + 5 × 80

= 53

Step 2:

Conversion: decimal to Hexadecimal

Read the remainder from bottom to top: (35)H

Therefore, the hexadecimal equivalent of octal number 658 : (35)H

Binary to Hexadecimal conversion table:

Tips and Tricks:

Every digit in octal represents 3 bits of binary and every digit in hexadecimal is 4 bits in binary

(65)8 = (110 101 )2

Forming pairs of 4 to get the hexadecimal representation, we get:

For the addition of two hexadecimal numbers, there are two methods:

• In the 1^st method, we first convert the hexadecimal number to decimal then add both numbers. After that, we convert that decimal number to hexadecimal number. But it is a time-consuming method and also calculations become bulky.
• In the 2^nd method, we directly add both hexadecimal numbers as shown below

Step 1: Divide (32)₁₀ successively by 16 until the quotient is 0.

\({32\over 16}=2\), the remainder is 0

\({2\over 16}=0\), the remainder is 2

Step 2: Read from the bottom (MSB) to the top (LSB) as 20.

So, 20 is the hexadecimal equivalent of the decimal number 32 

Concept:

Step 1: Conversion: Octal to decimal

Step 2: Conversion: decimal to Hexadecimal

Calculation:

Step 1:

Conversion: Octal to decimal

(657)8 = 6 × 82 + 5 × 8 + 7 × 80

= 431

Step 2:

Conversion: decimal to Hexadecimal

Read the remainder from bottom to top: (1AF) H

Therefore, the hexadecimal equivalent of octal number 6578 : (1AF) H

Binary to Hexadecimal conversion table:

Tips and Tricks:

Every digit in octal represents 3 bits of binary and every digit in hexadecimal is 4 bits in binary

(657)8 = (110 101 111)2

Forming pairs of 4 to get the hexadecimal representation, we get:

STEPS:

1) First, convert the given hexadecimal number into binary equivalent.

2) Convert that binary number into an octal number.

Binary equivalent of BCA9: 1011110010101001

Representation of this binary equivalent to octal number system is: 136251

Tips and Tricks:

For hexadecimal number, pair of 4 binary bits are taken from right to left and for octal number, pair of 3 binary bits is taken starting from least significant bits.

The correct answer is option 3.

Concept:

• In the 1st method, If we add both numbers after converting the hexadecimal number to decimal. The decimal number is then converted to a hexadecimal number. However, it is a time-consuming procedure, and the computations grow cumbersome as a result.
• In the 2nd method,  As demonstrated below, we just add both hexadecimal numbers together.

The given two Hexadecimal numbers are,

Hence the correct answer is (1B9)16.

For any number system with the radix (base) r, the allowed numbers are from 0 to (r – 1).

• For the binary system, the radix is 2 and the numbers used in this system are 0 and 1
• For the octal system, the radix is 8 and the numbers used in this system are 0 to 7
• For the decimal system, radix is 10 and the numbers used in this system are 0 to 9
• For the Hexadecimal system, radix is 16 and the numbers used in this system are 0 to F

Explanation:

• The hexadecimal number system consists of the symbols 0 - 9, A - F.
• Hexadecimal uses decimal numbers and six extra symbols.
• There are no numerical symbols that represent values greater than nine, so letters taken from the English alphabet are used, specifically A, B, C, D, E, and F, where Hexadecimal A = decimal 10, and hexadecimal F = decimal 15.
• A binary number is just a string of zeros and ones: 11011011.
• Three bits, each being on or off, can represent the eight numbers from 0 to 7, this is known as the octal number system.

Hence 7 is represented as 0111.

Important Points

Steps to Convert Binary to Hex:

• ​Start from the least significant bit (LSB) at the right of the binary number and divide it up into groups of 4 digits. (4 digital bits is called a "nibble").
• Convert each group of 4 binary digits to its equivalent hex value (see table above).
• Concatenate the results together, giving the total hex number.