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

Formula: 
A XOR B ≡ A ⊕ B ≡  A̅.B + A.B̅ 

XOR: Truth Table 

Option 1: Incorrect

Fails for input (A = 0, B = 0)

Since Output is 0

Option 2: Incorrect

Fails for input (A = 1, B = 1)

Since Output is 0

Option 3: correct

Valid all the cases of truth table

Option 4: Incorrect

Fails for input (A = 1, B = 1)

Since Output is 0

Encoder:

An encoder has 2ⁿ input lines and n output lines. In the encoder, the output lines generate the binary code corresponding to the input value which is active high.

Decoder:

It is a multi-input and multi-output logic circuit that converts coded inputs into coded outputs where input and output codes are different. Input code has fewer bits than output code. There is one to one mapping from input to output.

Multiplexer:

It is a digital switch. It allows digital information from several sources to be routed onto a single output line. A basic multiplexer has several data input lines and a single output line. The selection of a particular input line is controlled by selection lines. It is many to one mapping and provides the digital equivalent of an analog selector switch. Therefore it is the correct answer

Demultiplexer:

It is a circuit that receives information on a single line and transmits information on one of the 2ⁿ output lines. Selection of output line is controlled by values of n selection lines. 

F (P, Q, R, S) = ∑ 0, 2, 5, 7, 8, 10, 13, 15

Don’t care min terms are 2, 7, 8, 13

By plotting the K-map, the minimal SOP (sum of products) can be found.

Explanation –

While putting the terms to k-map following things happen,

• 3^rd and 4^th columns are swapped
• 3^rd and 4^th rows.
• term 2 is going to (0, 3) column instead of (0, 2)
• 8 is going to (3, 0) instead of (2,0)

Solving, the above K-map, we get Q̅S̅ + QS

The correct answer is 171661

 Key Points

• To find the octal equivalent of a hexadecimal number, you can convert each hexadecimal digit to its binary equivalent and then group the binary digits into groups of three (since each octal digit represents three binary digits).
• Let's convert each hexadecimal digit of (F3B1)16 to binary:
  • F = 1111
  • 3 = 0011
  • B = 1011
  • 1 = 0001
• Now group the binary digits into sets of three:
  • 1111 0011 1011 0001
• Now convert each set of three binary digits to octal:
  • 001 111 001 110 110 001
• Combine these octal digits: 171661.

Therefore, the octal equivalent of (F3B1)16 is option 3) 171661.

The correct answer is ASCII.

Key Points

• ASCII (American Standard Code for Information Interchange) is a character encoding standard for electronic communication.
• ASCII codes represent text in computers, telecommunications equipment, and other devices that use text.
• Originally based on the English alphabet, ASCII encodes 128 specified characters into seven-bit integers.
• This includes 33 non-printing control characters (which affect how text and space are processed) and 95 printable characters (including space).

Additional Information

• BCD (Binary-Coded Decimal) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of binary digits, usually four or eight.
• EBCDIC (Extended Binary Coded Decimal Interchange Code) is an eight-bit character encoding used mainly on IBM mainframe and IBM midrange computer operating systems.
• GRAY code, also known as reflected binary code, is a binary numeral system where two successive values differ in only one bit, which is used in error correction in digital communications.

• 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)

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

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.