Digital Logic MCQ Quiz - Objective Question with Answer for Digital Logic - Download Free PDF

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.

Concept: 

JK flip flop:

The truth table of JK flipflop:

T flip-flop is formed by combining both J and K inputs of the JK-flipflop

In the above truth table when J = K = 1, its output is toggled.

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Characteristic Table of JK flip flop

Qn+1 = JQ̅n + K̅Qn

The correct answer is C' + D'

Key PointsTo simplify the Boolean function F(A, B, C, D) using the Karnaugh Map (K-map) method, we first need to construct a 4-variable K-map and then fill in the values based on the given minterms (0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14). The minterms can be represented in binary form to determine their positions on the K-map.

The K-map for F(A, B, C, D) would look like this:

simplified expression =C’ + D’

Hence the correct answer is C’ + D’

De-multiplexer:

• The demultiplexer is a combinational logic circuit designed to switch one common input line to one of several separate output lines.
• The data distributor, known as a Demultiplexer or “Demux”, works in just the opposite way to that of the Multiplexer.
• The demultiplexer takes one single input data line and then switches it to any one of a number of individual output lines one at a time.
• A demultiplexer circuit is a decoder circuit with enable input.

The block diagram is as shown:

Application:

The demultiplexer converts a serial data signal at the input to parallel data at its output lines as shown below.

The function of the Demultiplexer is to switch one common data input line to any one of the 4 output data lines A to D.

Important Points

Multiplexer:

The multiplexer is a combinational logic circuit designed to switch one of several input lines to a single common output line.

• The multiplexer or “MUX” is a combinational logic circuit designed to switch one of several input lines through a single common output line by the application of a control signal.
• Multiplexers operate like very fast acting multiple position rotary switches connecting or controlling multiple input lines called “channels” one at a time to the output.
• Multiplexers are used to convert parallel to serial data.

• 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.

Binary 110110101 is equal to decimal 437

Calculation:

1 1 0 1 1 0 1 0 1

From rightmost first column as follows

=> (2⁰ * 1) + (2¹ * 0) + (2² * 1) + (2³ * 0) + (2⁴ * 1) + (2⁵ * 1) + (2⁶ * 0) + (2⁷ * 1) + (2⁸ * 1)

=> (1) + (0) + (4) + (0) + (16) + (32) + (0) + (128) + (256)

Decimal value =>437

The correct answer is 11000110

Key Points

• To convert the hexadecimal number C6 to a binary number, you can convert each hexadecimal digit to its 4-bit binary representation.
• C in hexadecimal is 12 in decimal, which is 1100 in binary.
• 6 in hexadecimal is 6 in decimal, which is 0110 in binary.
• So, the binary representation of C6 is 11000110.

Additional InformationHere are the decimal numbers 1 to 15 represented in both hexadecimal and binary forms:

•  Decimal 1: Hexadecimal 1, Binary 0001
• Decimal 2: Hexadecimal 2, Binary 0010
• Decimal 3: Hexadecimal 3, Binary 0011
• Decimal 4: Hexadecimal 4, Binary 0100
• Decimal 5: Hexadecimal 5, Binary 0101
• Decimal 6: Hexadecimal 6, Binary 0110
• Decimal 7: Hexadecimal 7, Binary 0111
• Decimal 8: Hexadecimal 8, Binary 1000
• Decimal 9: Hexadecimal 9, Binary 1001
• Decimal 10: Hexadecimal A, Binary 1010
• Decimal 11: Hexadecimal B, Binary 1011
• Decimal 12: Hexadecimal C, Binary 1100
• Decimal 13: Hexadecimal D, Binary 1101
• Decimal 14: Hexadecimal E, Binary 1110
• Decimal 15: Hexadecimal F, Binary 1111 

The sum of two binary numbers 1101111 and 1100101 is (11010100)₂

Note: In Binary addition, 1 + 1 = 10 (0 is sum value and 1 is carry), 1 + 0 = 1, 0 + 1 = 1 and 0 + 0 = 0.

Calculation:

  1    1 1 1 1        (Carry values)

  1 1 0 1 1 1 1     (Binary number 1)

  0    1 0 0 0        (Sum values)

+1 1 0 0 1 0 1     (Binary number 2)

-------------------

1 1 0 1 0 1 0 0    (Answer)

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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.

So Octal Equivalent: 1353

Important Points

Binary to Octal code

Calculation:

14 in binary form is represented as:

1410 = (00001110)2

Taking the 1's complement of the above, we get 11110001

Adding 1 to the 1's complement, we get the 2's complement representation of the number, i.e. 11110010

Since there is a 1 in the MSB, the number is a negative number with value -14.

∴ The 2's complement of -6410 contains 7 bits.

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 correct answer is (11010)2 = (62)8

Key Points

Binary numbers and octal numbers are both used in computing. They are different ways of representing the same value - just like how "10" and "ten" are different ways of expressing the same quantity in decimal.

• Each digit of an octal number represents three binary digits because 2³ = 8. Here's the mapping:
  • "000" => "0"
  • "001" => "1"
  • "010" => "2"
  • "011" => "3"
  • "100" => "4"
  • "101" => "5"
  • "110" => "6"
  • "111" => "7"
• Now let's convert the binary numbers to their equivalent octal numbers.
  • (111 110 111)₂ = (7 6 7)₈
  • (110 110 101)₂ = (6 6 5)₈
  • (10 101 . 110)₂ = (2 5 . 6)₈
  • (11 010)₂ = (3 2)₈ - Corrupted as the corresponding octal number should be (32)₈ instead of (62)₈.

Therefore, the 4th pair, (11010)₂ = (62)₈, is not equal.