# Gate/GATE STUDY MATERIAL Sample Test,Sample questions

1.5

2.6

3.7

4.8

1.4 time units

2.6 time units

3.10 time units

4.12 time units

1.1

2.2

3.3

4.4

## Question: ``` Consider the operations f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(Xâ€², Y, Z) = Xâ€²YZ + Xâ€²YZâ€² + XY. Which one of the following is correct?```

1.Both {f} and {g} are functionally complete

2.Only {f} is functionally complete

3.Only {g} is functionally complete

4.Neither {f} nor {g} is functionally complete

1.PQ'

2.PR'

3.PQ' + R

4.PR'' + Q

## Question: ``` In an SR latch made by cross-coupling two NAND gates, if both S and R inputs are set to 0, then it will result in```

1.Q = 0, Q' = 1

2.Q = 1, Q' = 0

3.Q = 1, Q' = 1

4. Indeterminate states

1.x' + y'

2.x + y

3.x + y'

4.x' + y

1.1AF

2.D78

3.D71

4.32F

## Question: ``` The minterm expansion of f(P, Q, R) = PQ + QR' + PR' is ```

1.m2 + m4 + m6 + m7

2.m0 + m1 + m3 + m5

3.m0 + m1 + m6 + m7

4.m2 + m3 + m4 + m5

## Question: ``` Using a 4-bit 2â€™s complement arithmetic, which of the following additions will result in an overflow? (i) 1100 + 1100 (ii) 0011 + 0111 (iii) 1111 + 0111```

1.(i) only

2. (ii) only

3.(iii) only

4. (i) and (iii) only

1.2

2.3

3.4

4.5

1.2

2.3

3.4

4.5

## Question: `A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate. The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4-bit ripple-carry binary adder is implemented by using full adders. The total propagation time of this 4-bit binary adder in microseconds is`

1.19.2 microseconds

2.18.0 microseconds

3.12.3 microseconds

4.16.6 microseconds

1.1, 1, 0

2. 1, 0, 0

3.0, 1, 0

4.1, 0, 1

## Question: `Consider a 4 bit Johnson counter with an initial value of 0000. The counting sequence of this counter is:`

1.0, 1, 3, 7, 15, 14, 12, 8, 0

2.0, 1, 3, 5, 7, 9, 11, 13, 15, 0

3. 0, 2, 4, 6, 8, 10, 12, 14, 0

4. 0, 8, 12, 14, 15, 7, 3, 1, 0

## Question: `Consider a Boolean function f (w, x, y, z). suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i1 = (w1, x1, y1, z1) and i2 = (w2, x2, y2, z2) we would like the function to remain true as the input changes from i1 to i2 (i1 and i2 differ in exactly one bit position), without becoming false momentarily. Let f (w, x, y, z) = âˆ‘(5,7,11,12,13,15). Which of the following cube covers of f will ensure that the required property is satisfied?`

1.w'xz, wxy', xy'z, xyz,wyz

2.wxy,w'xz,wyz

3.wx(yz)', xz, wx'yz

4.wzy, wyz, wxz, w'xz, xy'z, xyz

1.Î˜(1)

2. Î˜(Log (n))

3. Î˜(âˆš n)

4. Î˜(n)

## Question: `Consider a multiplexer with X and Y as data inputs and Z as control input. Z = 0 selects input X, and Z = 1 selects input Y. What are the connections required to realize the 2-variable Boolean function f = T + R, without using any additional hardware ?`

1.R to X, 1 to Y, T to Z

2.T to X, R to Y, T to Z

3.T to X, R to Y, 0 to Z

4.R to X, 0 to Y, T to Z

1.Î˜(1)

2. Î˜(log n)

3.Î˜(n)

4. Î˜(n^2)

1.-1

2.2

3.1

4.-2

## Question: `Consider the following Boolean function of four variables: f(w,x,y,z) = âˆ‘(1,3,4,6,9,11,12,14) The function is:`

1.independent of one variables

2.independent of two variables

3. independent of three variables

4. dependent on all the variables

## Question: ```Consider the following combinational function block involving four Boolean variables x, y, a, b where x, a, b are inputs and y is the output. f (x, y, a, b) { if (x is 1) y = a; else y = b; } Which one of the following digital logic blocks is the most suitable for implementing this function?```

2.Priority encoder

3.Multiplexer

4.Flip-flop

## Question: ```Define the connective * for the Boolean variables X and Y as: X * Y = XY + X' Y'. Let Z = X * Y. Consider the following expressions P, Q and R. P: X = Yâ‹†Z Q: Y = Xâ‹†Z R: Xâ‹†Yâ‹†Z=1 Which of the following is TRUE?```

1.Only P and Q are valid

2.Only Q and R are valid

3.Only P and R are valid

4.All P, Q, R are valid

## Question: ```Given the function F = Pâ€² + QR, where F is a function in three Boolean variables P, Q and R and Pâ€² = !P, consider the following statements. S1: F = Î£ (4, 5, 6) S2: F = Î£ (0, 1, 2, 3, 7) S3: F = Î  (4, 5, 6) S4: F = Î  (0, 1, 2, 3, 7) Which of the following is true?```

1.S1-False, S2-True, S3-True, S4-False

2.S1-True, S2-False, S3-False, S4-True

3.S1-False, S2-False, S3-True, S4-True

4.S1-True, S2-True, S3-False, S4-False

1.7

2.8

3.9

4.10

1.134

2.133

3.124

4.123

1.6, 3

2.10, 4

3. 6, 4

4. 10, 5

1.x' + z

2.xyz

3.xy' + z

4.None of these

## Question: ```Let f(w, x, y, z) = âˆ‘(0, 4, 5, 7, 8, 9, 13, 15). Which of the following expressions are NOT equivalent to f? ```

1.x'y'z' + w'xy' + wy'z + xz

2.w'y'z' + wx'y' + xz

3.w'y'z' + wx'y' + xyz + xy'z

4.x'y'z' + wx'y' + w'y

## Question: `Let k = 2^n. A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2^n bit decoder. This circuit is equivalent to a`

1.k-bit binary up counter

2.k-bit binary down counter

3.k-bit ring counter

4. k-bit Johnson counter

1.1

2.2

3.3

4.0

1.P + Q

2. (P + Q)'

3. P X Q

4. (P X Q)'

## Question: `Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of n variables. What is the minimum size of the multiplexer needed?`

1.2^n line to 1 line

2.2^(n+1) line to 1 line

3. 2^(n-1) line to 1 line

4. 2^(n-2) line to 1 line

## Question: `The addition of 4-bit, two's complement, binary numbers 1101 and 0100 results in`

1.0001 and an overflow

2.1001 and no overflow

3.0001 and no overflow

4.1001 and an overflow

## Question: `The Boolean function x'y' + xy + x'y is equivalent to`

1.BC'D' + A'C'D + AB'D b. c. d.

2. ABC' + ACD + B'C'D

3. ACD' + A'BC' + AC'D'

4.A'BD + ACD' + BCD'

1. -10

2. -13

3. -26

4.None of These

## Question: `The function ABâ€™C + Aâ€™BC + ABCâ€™ + Aâ€™Bâ€™C + ABâ€™Câ€™ is equivalent to`

1.ACâ€™+AB+Aâ€™C

2.ABâ€™+ACâ€™+Aâ€™C

3.Aâ€™B+ACâ€™+AB'

4.Aâ€™B+AC+AB'

1.0

2.1

3.2

4.3

## Question: `The number (123456)8 is equivalent to`

1.(A72E)16 and (22130232)4

2.(A72E)16 and (22131122)4

3.(A73E)16 and (22130232)4

4.(A62E)16 and (22120232)4

1.1

2.2

3.3

4.4

1.(P'.Q + R')

2.(P + Q'.R')

3. (P'.Q + R)

4. (P.Q + R)

## Question: `The switching expression corresponding to f(A, B, C, D) = Î£ (1, 4, 5, 9, 11, 12) is`

1. BC'D' + A'C'D + AB'D

2. ABC' + ACD + B'C'D

3.ACD' + A'BC' + AC'D

4. A'BD + ACD' + BCD'

1.2

2.3

3.4

4.5

## Question: `Using Booth's Algorithm for multiplication, the multiplier -57 will be recoded as`

1.0 -1 0 0 1 0 0 -1

2.1 1 0 0 0 1 1 1

3.0 -1 0 0 1 0 0 0

4.0 1 0 0 -1 0 0 1

1.1

2.2

3.4

4.5

1.3

2.4

3.5

4.6

1.a'c and ac'

2. a'c and b'c

3.a'c only

4.ac' and bc'

## Question: `Which of the following expressions is equivalent to (AâŠ•B)âŠ•C`

1.(A+B+C)(AÂ¯+BÂ¯+CÂ¯)

2.(A+B+C)(AÂ¯+BÂ¯+C)

3.ABC+AÂ¯(BâŠ•C)+BÂ¯(AâŠ•C)

4.None of the above

1.11, 00

2. 01, 10

3. 10, 01

4. 00, 11

## Question: `Which one of the following expressions does NOT represent exclusive NOR of x and y?`

1.xy + x' y'

2.x ^ y' where ^ is XOR

3.x' ^ y where ^ is XOR

4.x' ^ y' where ^ is XOR

## More MCQS

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