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BPSC TRE · Computer Science

Digital Logic & Number Systems Previous Year Questions

29 Digital Logic & Number Systems (Computer Science) questions asked in BPSC TRE previous year papers, each with the correct answer and explanation. Read them free on UTpaper, or attempt the full papers as timed online tests.

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DBMS & SQL 48Data Structures 44Computer Networks 33Computer Organization & Architecture 27OOP 18Programming in C/C++ 16Operating Systems 14Algorithms 9
Q1BPSC TRE 2.0 (2023) Computer Class 9-10
When a key is pressed on keyboard, which standard is used for converting the keystroke into the corresponding bits?
  1. AANSI
  2. BASCII
  3. CEBCDIC
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) ANSI

Explanation

Note: the official key gives (A) ANSI; the character code most commonly named for keystroke-to-bits conversion is ASCII (B). The key is kept as printed.

Q2BPSC TRE 2.0 (2023) Computer Class 9-10
The logic gate that provides high output for same input is
  1. ANOT
  2. BX-NOR
  3. CXOR
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) X-NOR

Explanation

XNOR gives output 1 when both inputs are equal.

Q3BPSC TRE 2.0 (2023) Computer Class 9-10
The simplified form of the Boolean expression (X + Y + XY)(X + Z) is
  1. AXY + YZ
  2. BX + YZ
  3. CXZ + Y
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) X + YZ

Explanation

X + Y + XY = X + Y, and (X + Y)(X + Z) = X + YZ by the distributive law.

Q4BPSC TRE 2.0 (2023) Computer Class 9-10
The dual of a Boolean expression is obtained by
  1. Ainterchanging all 0s and 1s
  2. Binterchanging all 0s and 1s, all + and '.' signs
  3. Cinterchanging all 0s and 1s, all + and '.' signs and complementing all the variables
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) interchanging all 0s and 1s, all + and '.' signs

Explanation

The dual is formed by swapping 0 and 1 and also swapping + with '.', without complementing the variables.

Q5BPSC TRE 3.0 (2024) Computer Science Class 11-12
Digital circuit can be made by the repeated use of the _________.
  1. ANAND gate
  2. BNOR gate
  3. CAND gate
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (D) More than one of the above

Explanation

NAND and NOR are both universal gates, so any digital circuit can be built by repeatedly using either one. AND alone is not universal.

Q6BPSC TRE 3.0 (2024) Computer Science Class 11-12
When does a negative level triggered flip-flop in Digital Electronics changes its state?
  1. AWhen the clock is Negative
  2. BWhen the clock is Positive
  3. CWhen the inputs are all zero
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) When the clock is Negative

Explanation

A negative (low) level-triggered flip-flop responds to its inputs and can change state only while the clock is at its low (0) level.

Q7BPSC TRE 3.0 (2024) Computer Science Class 11-12
What is the result of the operation 1010 AND 1100 in binary?
  1. A1000
  2. B1110
  3. C100
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) 1000

Explanation

Bitwise AND gives 1 only where both bits are 1: 1010 AND 1100 = 1000.

Q8BPSC TRE 3.0 (2024) Computer Science Class 11-12
Convert the decimal number 1234 to binary, octal, and hexadecimal. Which of the following options correctly represents these conversions?
  1. ABinary: 10011010010, Octal: 2322, Hexadecimal: 4D2
  2. BBinary: 11001110010, Octal: 1712, Hexadecimal: 72A
  3. CBinary: 11100110010, Octal: 1642, Hexadecimal: 3CD
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) Binary: 10011010010, Octal: 2322, Hexadecimal: 4D2

Explanation

1234 = 4×256 + 13×16 + 2, so it is 4D2 in hex. In octal, 2×512 + 3×64 + 2×8 + 2 = 1234 gives 2322, and binary 100 1101 0010 is 10011010010.

Q9BPSC TRE 3.0 (2024) Computer Science Class 11-12
When performing BCD addition, what is the maximum value that can be represented in a single BCD digit?
  1. A2
  2. B10
  3. C15
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (E) None of the above

Explanation

A BCD digit uses 4 bits but only codes 0 to 9, so its maximum value is 9. That is not among the options; any sum above 9 needs +6 correction.

Q10BPSC TRE 3.0 (2024) Computer Science Class 11-12
Convert the binary number 1011.1101 to its decimal equivalent. Which of the following is the correct decimal value?
  1. A11.75
  2. B12.125
  3. C13.5
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (E) None of the above

Explanation

1011 = 11, and .1101 = 0.5 + 0.25 + 0 + 0.0625 = 0.8125, so the value is 11.8125. None of the listed values matches.

Q11BPSC TRE 3.0 (2024) Computer Science Class 11-12
What is De Morgan’s theorem used for in digital logic?
  1. ASimplifying Boolean expressions
  2. BImplementing NAND gates
  3. CPerforming binary addition
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (D) More than one of the above

Explanation

De Morgan's theorems, (AB)' = A' + B' and (A + B)' = A'B', are used to simplify Boolean expressions and to turn circuits into NAND/NOR-only forms, so both A and B are correct.

Q12BPSC TRE 1.0 (2023) Computer Science Class 11-12
What are the canonical forms of Boolean expressions?
  1. AOR and XOR
  2. BNOR and XNOR
  3. CSOM and POM
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (C) SOM and POM

Explanation

The canonical forms are sum of minterms (SOM, or canonical SOP) and product of maxterms (POM, or canonical POS).

Q13BPSC TRE 1.0 (2023) Computer Science Class 11-12
Derive the Boolean expression for the logic circuit shown below:
  1. AC(A + B)DE
  2. B[C(A + B)D + E′]
  3. C[[C(A + B)D]E′]
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) C(A + B)DE

Explanation

The circuit gives A + B from the OR gate, then three AND gates in turn multiply it by C, D and E. So Y = C(A + B)DE, with E not inverted.

Q14BPSC TRE 1.0 (2023) Computer Science Class 11-12
Boolean algebra can be used
  1. Afor designing the digital computers
  2. Bin building logic symbols
  3. Cin circuit theory
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (D) More than one of the above

Explanation

Boolean algebra is used in designing digital computers, in building logic symbols and gates, and in switching circuit theory, so more than one option applies.

Q15BPSC TRE 1.0 (2023) Computer Science Class 11-12
To display time in railway stations which digital circuit is used?
  1. ASeven-segment decoder
  2. BEight-segment encoder
  3. C8 : 3 multiplexer
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) Seven-segment decoder

Explanation

Digital clocks at stations show digits on seven-segment displays, which are driven by seven-segment (BCD-to-7-segment) decoders.

Q16BPSC TRE 2.0 (2023) Computer Science Class 11-12
The cost of storing a bit is minimum in
  1. Acache
  2. Bregister
  3. Cmagnetic tape
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (C) magnetic tape

Explanation

Magnetic tape is the cheapest storage per bit, and also the slowest. Registers and cache are the fastest and most expensive, so they cost the most per bit.

Q17BPSC TRE 2.0 (2023) Computer Science Class 11-12
The register that contains the address of the next instruction to be executed is called
  1. Aprogram counter
  2. Binstruction register
  3. Caccumulator
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) program counter

Explanation

The program counter (PC) holds the address of the next instruction to be fetched. It is incremented after each fetch.

Q18BPSC TRE 2.0 (2023) Computer Science Class 11-12
The register that contains the instruction that is being executed is called
  1. Aaccumulator
  2. Bprogram counter
  3. Cinstruction register
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (C) instruction register

Explanation

The instruction register (IR) holds the instruction that is currently being decoded and executed.

Q19BPSC TRE 2.0 (2023) Computer Science Class 11-12
The number of 1’s in the binary representation of the value of the decimal expression 16³ × 9 + 16² × 7 + 16 × 5 + 3 is
  1. A15
  2. B9
  3. C12
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) 9

Explanation

The expression is (9753)₁₆ = 1001 0111 0101 0011₂. The 1s per group are 2 + 3 + 2 + 2 = 9.

Q20BPSC TRE 2.0 (2023) Computer Science Class 11-12
The Boolean expression x + x′y equals
  1. Ax + y
  2. Bx + xy
  3. Cy + yx
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) x + y

Explanation

x + x′y = (x + x′)(x + y) = 1·(x + y) = x + y, using the distributive law.

Q21BPSC TRE 2.0 (2023) Computer Science Class 11-12
The Boolean expression AB + AB′ + A′C + AC is independent of Boolean variable
  1. AA
  2. BB
  3. CC
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) B

Explanation

AB + AB′ = A(B + B′) = A, and A + A′C + AC = A + C. The result A + C does not contain B.

Q22BPSC TRE 2.0 (2023) Computer Science Class 11-12
The Boolean expression A + BC equals
  1. A(A′ + B)(A′ + C)
  2. B(A + B)(A′ + C)
  3. C(A + B)(A + C)
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (C) (A + B)(A + C)

Explanation

By the distributive law of Boolean algebra, A + BC = (A + B)(A + C).

Q23BPSC TRE 2.0 (2023) Computer Science Class 11-12
The Boolean expression x + xy will be equal to
  1. Ax
  2. By
  3. Cx + y
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) x

Explanation

By the absorption law, x + xy = x(1 + y) = x.

Q24BPSC TRE 2.0 (2023) Computer Science Class 11-12
The Boolean expression x(x + y) is equal to
  1. Ax
  2. By
  3. Cxy
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) x

Explanation

By absorption, x(x + y) = x + xy = x.

Q25BPSC TRE 2.0 (2023) Computer Science Class 11-12
If x is a Boolean variable, then (((x′)′)′)′ will be
  1. Ax′
  2. Bx
  3. Cx + x′
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) x

Explanation

There are four complements in a row, an even number, so they cancel out and the result is x.

Q26BPSC TRE 2.0 (2023) Computer Science Class 11-12
In two-valued Boolean algebra, the maximum number of Boolean functions for two variables will be
  1. A8
  2. B12
  3. C16
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (C) 16

Explanation

With n variables there are 2^(2ⁿ) Boolean functions. For n = 2 that is 2⁴ = 16.

Q27BPSC TRE 2.0 (2023) Computer Science Class 11-12
Simplified Boolean function of Boolean function F = A′C + A′B + AB′C + BC is
  1. AF = C + A′B
  2. BF = A′B + B′C
  3. CF = BC + A′B
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (A) F = C + A′B

Explanation

F covers minterms 1, 2, 3, 5 and 7. Minterms 1, 3, 5 and 7 group to C, and 2 and 3 group to A′B, so F = C + A′B.

Q28BPSC TRE 2.0 (2023) Computer Science Class 11-12
Which of the following logic gates is called universal gate?
  1. AAND
  2. BOR
  3. CNAND
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (C) NAND

Explanation

NAND (like NOR) is a universal gate, because AND, OR and NOT can all be built from NAND gates alone.

Q29BPSC TRE 2.0 (2023) Computer Science Class 11-12
The minimum number of NAND gates required to implement Boolean function f = x′y + xy′ is
  1. A3
  2. B4
  3. C6
  4. DMore than one of the above
  5. ENone of the above
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Correct answer: (B) 4

Explanation

x′y + xy′ is XOR, and XOR needs at least 4 NAND gates. One NAND makes (xy)′, two NANDs combine it with x and with y, and a fourth NAND joins their outputs.

How to use these BPSC TRE Computer Science questions

Every question here was asked in a real BPSC TRE paper; the paper and shift are shown on the card, and the number opens the question on its own page. Try each one before tapping Show answer, then attempt the full BPSC TRE papers as timed tests to check your speed under exam conditions.

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