Chapter 5: Number System and Digital Logic (Set-6)
In a positional number system, the value of a digit depends mainly on its base and its position within the number. Which concept explains this idea clearly?
A Parity rule
B Gray coding
C Bit masking
D Place value
Explanation: In positional systems, each digit’s value equals digit × (base power of its position). This positional weight system allows the same digit to represent different values depending on its location.
The decimal number system uses ten unique symbols from 0 to 9. What is its radix?
A 10
B 2
C 8
D 16
Explanation: Radix means base of a number system. Decimal system uses ten digits (0–9), so its base or radix is 10, and each position represents powers of 10.
In binary number system, how many different digits are used to represent all values?
A One digit
B Two digits
C Eight digits
D Ten digits
Explanation: Binary uses only 0 and 1. These two symbols represent all possible values in digital systems, forming the foundation of computer hardware and digital logic design.
Which number system is most suitable for representing internal data in digital computers?
A Decimal
B Octal
C Binary
D Roman
Explanation: Computers use electronic circuits that have two stable states (on/off). These states are naturally represented using binary digits 0 and 1.
A hexadecimal digit can represent how many distinct decimal values?
A 16 values
B 8 values
C 10 values
D 15 values
Explanation: Hexadecimal uses digits 0–9 and letters A–F. That makes 16 different symbols, representing decimal values from 0 to 15.
In binary, the rightmost bit is known as the least significant bit because it has the lowest power of 2. Which power does it represent?
A 2¹
B 2²
C 2³
D 2⁰
Explanation: The least significant bit (LSB) represents 2⁰, which equals 1. It contributes the smallest value to the overall number in binary representation.
Convert decimal 15 into binary form.
A 1110
B 1011
C 1111
D 1101
Explanation: 15 equals 8 + 4 + 2 + 1. Therefore, all four lower binary bits are 1, giving 1111₂.
In octal system, each digit corresponds exactly to how many binary bits?
A 2 bits
B 4 bits
C 3 bits
D 5 bits
Explanation: Since octal base is 8 and 2³ = 8, each octal digit maps directly to 3 binary bits.
Convert hexadecimal F into decimal value.
A 12
B 13
C 14
D 15
Explanation: In hexadecimal, A=10, B=11, C=12, D=13, E=14, F=15. So F represents decimal 15.
In unsigned 4-bit binary, what is the highest possible value?
A 7
B 8
C 15
D 14
Explanation: Maximum unsigned value with 4 bits is 2⁴−1 = 16−1 = 15, represented as 1111₂.
The process of adding 1 to the 1’s complement of a number produces which form?
A Gray code
B 2’s complement
C BCD form
D Sign magnitude
Explanation: 2’s complement is obtained by inverting all bits (1’s complement) and then adding 1. It is widely used for signed number representation.
In 2’s complement representation, the most significant bit primarily indicates what?
A Sign bit
B Carry bit
C Parity bit
D Borrow bit
Explanation: In signed 2’s complement numbers, MSB acts as sign bit. 0 indicates positive or zero, and 1 indicates a negative number.
Binary addition of 1 + 1 gives what result?
A 1
B 11
C 10
D 0
Explanation: 1 + 1 equals 2 in decimal, which is written as 10 in binary. The result has sum 0 and carry 1.
A logic gate that produces output 1 only when both inputs are 1 is called?
A OR gate
B XOR gate
C NOR gate
D AND gate
Explanation: AND gate outputs 1 only when all inputs are 1. If any input is 0, output becomes 0.
A gate that inverts its input value is known as?
A NOT gate
B XOR gate
C NAND gate
D AND gate
Explanation: NOT gate, also called inverter, outputs complement of input. If input is 1, output becomes 0 and vice versa.
The output of OR gate is 0 only when?
A All inputs 1
B Any input 1
C All inputs 0
D Inputs differ
Explanation: OR gate gives output 1 if at least one input is 1. It outputs 0 only when all inputs are 0.
NAND gate is called universal gate because it can implement?
A Only AND
B Only OR
C Only NOT
D Any logic function
Explanation: NAND gate can be combined to create AND, OR, NOT and all other Boolean functions. Therefore, it is known as a universal gate.
Boolean algebra works with how many logic values?
A One value
B Two values
C Three values
D Four values
Explanation: Boolean algebra uses two logic values: 0 (false) and 1 (true). These values represent digital signals in logic circuits.
According to identity law, A + 0 equals?
A 0
B 1
C A
D A’
Explanation: Identity law states that OR with 0 leaves the variable unchanged. So A + 0 equals A.
In Boolean algebra, A · 1 equals?
A A
B 0
C 1
D A’
Explanation: AND with 1 does not change the variable. Therefore, A · 1 equals A.
Complement rule states that A + A’ equals?
A 0
B A
C 1
D A’
Explanation: A OR its complement always equals 1 because one of them must be true.
A truth table for 2 input variables contains how many rows?
A 2
B 4
C 3
D 8
Explanation: For n variables, rows = 2ⁿ. With 2 variables, 2² = 4 rows are needed.
Half adder circuit produces which two outputs?
A Sum and Borrow
B Input and Output
C Set and Reset
D Sum and Carry
Explanation: Half adder adds two bits and gives sum and carry outputs. It does not handle carry-in.
Full adder differs from half adder because it has?
A No carry
B Only one input
C Carry-in input
D No output
Explanation: Full adder adds three bits (two data bits and one carry-in). It supports multi-bit addition.
A multiplexer selects data based on?
A Select lines
B Data lines
C Output lines
D Power lines
Explanation: Select lines determine which input is connected to output in a multiplexer.
A demultiplexer distributes one input into?
A One output
B No output
C Two inputs
D Many outputs
Explanation: A demultiplexer routes single input to one of many outputs depending on select lines.
BCD code is mainly used to represent?
A Binary digits
B Hex digits
C Decimal digits
D ASCII letters
Explanation: BCD represents each decimal digit (0–9) using 4-bit binary code.
Even parity ensures total number of 1s is?
A Even
B Odd
C Zero
D Prime
Explanation: Even parity bit is added so total count of 1 bits becomes even, helping detect single-bit errors.
ASCII code is mainly used for representing?
A Colors
B Characters
C Images
D Signals
Explanation: ASCII assigns numeric codes to letters, digits, and symbols for text representation.
A binary code in which two successive values differ by only one bit is known as?
A BCD code
B ASCII code
C Gray code
D Excess-3
Explanation: Gray code is designed so adjacent numbers differ by only one bit. This reduces errors in mechanical position encoders and digital systems during state transitions.
In Excess-3 code, each decimal digit is represented by adding which value to its BCD equivalent?
A 3
B 1
C 2
D 6
Explanation: Excess-3 is formed by adding 3 (0011₂) to each decimal digit’s 4-bit BCD representation. It is a self-complementing code used in digital arithmetic.
The output of XOR gate for inputs 1 and 0 is?
A 0
B 10
C 11
D 1
Explanation: XOR outputs 1 when inputs are different. Since 1 and 0 are different, the result is 1.
In Boolean algebra, the expression A · A simplifies to?
A 0
B 1
C A
D A’
Explanation: According to idempotent law, A · A equals A. Repeating the same variable in AND operation does not change its value.
The Boolean expression A + A simplifies to?
A 0
B A
C 1
D A’
Explanation: By idempotent law, A + A equals A. OR-ing a variable with itself does not change its value.
Which logic gate outputs 1 only when inputs are different?
A AND gate
B OR gate
C NOR gate
D XOR gate
Explanation: XOR gate outputs 1 only when inputs differ. It is commonly used in adders and parity generation circuits.
The binary equivalent of decimal 32 is?
A 100000
B 10000
C 110000
D 10010
Explanation: 32 equals 2⁵. So in binary, it is represented as 1 followed by five zeros: 100000₂.
How many cells are there in a 3-variable Karnaugh map?
A 4
B 6
C 8
D 16
Explanation: A K-map contains 2ⁿ cells for n variables. For 3 variables, 2³ = 8 cells are required.
In Karnaugh map grouping, groups must contain how many cells?
A Any number
B Power of two
C Prime number
D Exactly four
Explanation: Valid K-map groups contain 1, 2, 4, 8, etc., cells. These sizes allow proper elimination of variables during simplification.
The binary multiplication 101 × 10 equals?
A 1010
B 1110
C 1001
D 1100
Explanation: Multiplying by 10₂ shifts the number left by one position. So 101₂ becomes 1010₂, which equals decimal 10.
In digital circuits, combinational logic depends only on?
A Past outputs
B Clock pulse
C Memory state
D Present inputs
Explanation: Combinational circuits have no memory. Their output depends only on current input values.
Sequential logic circuits differ because they include?
A Only gates
B No inputs
C Memory elements
D Only outputs
Explanation: Sequential circuits contain memory elements like flip-flops, so their output depends on both current inputs and previous states.
The smallest unit of digital information is called?
A Bit
B Byte
C Nibble
D Word
Explanation: A bit (binary digit) is the smallest unit of information and can have value 0 or 1.
A group of 8 bits is known as?
A Nibble
B Byte
C Word
D Parity
Explanation: Eight bits form one byte. It is commonly used to represent a character in computers.
In 2’s complement system, subtraction is performed by?
A Direct subtraction
B Multiplying values
C Adding complement
D Dividing values
Explanation: Subtraction A − B is performed by adding the 2’s complement of B to A. This simplifies hardware design.
A flip-flop stores how many bits of information?
A 2 bits
B 4 bits
C 8 bits
D 1 bit
Explanation: A flip-flop is a memory element that stores exactly one bit of data.
The output of XNOR gate is 1 when inputs are?
A Equal
B Different
C Both 0 only
D Both 1 only
Explanation: XNOR outputs 1 when inputs are the same (00 or 11). It is used in equality checking.
In Boolean algebra, the law A + 1 equals?
A 0
B 1
C A
D A’
Explanation: OR with 1 always results in 1 because at least one input is true.
In a 2-input AND gate, how many input combinations produce output 1?
A 2
B 3
C 1
D 4
Explanation: For inputs 00, 01, 10, 11, only 11 produces output 1 in AND gate.
Binary division by 2 is equivalent to performing which operation?
A Right shift
B Left shift
C XOR operation
D NOT operation
Explanation: Dividing a binary number by 2 shifts all bits one place to the right, reducing its value by half (ignoring fractions).