A 1-input, 2-output synchronous sequential circuit behaves as follows : Let zk, nk denote the number of 0's and 1's respectively in initial k bits of the input (zk + nk = k). The circuit outputs 00 until one of the following conditions holds. zk - nk = 2. In this case, the output at the k-th and all subsequent clock ticks is 10. nk - zk = 2. In this case, the output at the k-th and all subsequent clock ticks is 01. What is the minimum number of states required in the state transition graph of the above circuit?
1.5
2.6
3.7
4.8
A 4-bit carry lookahead adder, which adds two 4-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using two-level AND-OR logic.
1.4 time units
2.6 time units
3.10 time units
4.12 time units
Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is _____ .
1.1
2.2
3.3
4.4
Consider the operations f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X′, Y, Z) = X′YZ + X′YZ′ + 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
If P, Q, R are Boolean variables, then (P + Q')(PQ' + PR)(P'R' + Q') simplifies
1.PQ'
2.PR'
3.PQ' + R
4.PR'' + Q
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
The Boolean function x'y' + xy + x'y is equivalent to
1.x' + y'
2.x + y
3.x + y'
4.x' + y
The hexadecimal representation of 6578 is
1.1AF
2.D78
3.D71
4.32F
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
Using a 4-bit 2’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
What is the minimum number of gates required to implement the Boolean function (AB+C)if we have to use only 2-input NOR gates
1.2
2.3
3.4
4.5
A circuit outputs a digit in the form of 4 bits. 0 is represented by 0000, 1 by 0001, ..., 9 by 1001. A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit ≥ 5, and 0 otherwise. If only AND, OR and NOT gates may be used, what is the minimum number of gates required?
1.2
2.3
3.4
4.5
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
A processor that has carry, overflow and sign flag bits as part of its program status word (PSW) performs addition of the following two 2's complement numbers 01001101 and 11101001. After the execution of this addition operation, the status of the carry, overflow and sign flags, respectively will be:
1.1, 1, 0
2. 1, 0, 0
3.0, 1, 0
4.1, 0, 1
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
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) = ∑(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
Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is
1.Θ(1)
2. Θ(Log (n))
3. Θ(√ n)
4. Θ(n)
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
Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is
1.Θ(1)
2. Θ(log n)
3.Θ(n)
4. Θ(n^2)
Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _____________
1.-1
2.2
3.1
4.-2
Consider the following Boolean function of four variables: f(w,x,y,z) = ∑(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
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?1.Full adder
2.Priority encoder
3.Multiplexer
4.Flip-flop
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 = Y⋆Z Q: Y = X⋆Z R: X⋆Y⋆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
Given the function F = P′ + QR, where F is a function in three Boolean variables P, Q and R and P′ = !P, consider the following statements. S1: F = Σ (4, 5, 6) S2: F = Σ (0, 1, 2, 3, 7) S3: F = Π(4, 5, 6) S4: F = Π(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
How many 3-to-8 line decoders with an enable input are needed to construct a 6-to-64 line decoder without using any other logic gates?
1.7
2.8
3.9
4.10
How many pulses are needed to change the contents of a 8-bit up counter from 10101100 to 00100111 (rightmost bit is the LSB)?
1.134
2.133
3.124
4.123
In a look-ahead carry generator, the carry generate function Gi and the carry propagate function Pi for inputs Ai and Bi are given by: Pi = Ai ⨠Bi and Gi = AiBi The expressions for the sum bit Si and the carry bit Ci+1 of the look-ahead carry adder are given by: Si = Pi ⨠Ci and Ci+1 = Gi + PiCi , where C0 is the input carry. Consider a two-level logic implementation of the look-ahead carry generator. Assume that all Pi and Gi are available for the carry generator circuit and that the AND and OR gates can have any number of inputs. The number of AND gates and OR gates needed to implement the look-ahead carry generator for a 4-bit adder with S3, S2, S1, S0 and C4 as its outputs are respectively:
1.6, 3
2.10, 4
3. 6, 4
4. 10, 5
Let f(A, B) = A' + B. Simplified expression for function f(f(x + y, y)z) is :
1.x' + z
2.xyz
3.xy' + z
4.None of these
Let f(w, x, y, z) = ∑(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
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
Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X −Y is _________
1.1
2.2
3.3
4.0
Let X denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q: F(P, Q) = ( ( 1 X P) X (P X Q) ) X ( (P X Q) X (Q X 0) ) The equivalent expression for F is
1.P + Q
2. (P + Q)'
3. P X Q
4. (P X Q)'
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
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
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'
The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is
1. -10
2. -13
3. -26
4.None of These
The function AB’C + A’BC + ABC’ + A’B’C + AB’C’ is equivalent to
1.AC’+AB+A’C
2.AB’+AC’+A’C
3.A’B+AC’+AB'
4.A’B+AC+AB'
The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0, 0, 1, 1, 2, 2, 3, 3, 0, 0,...) is ________.
1.0
2.1
3.2
4.3
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
The number of min-terms after minimizing the following Boolean expression is _________. [D′ + AB′ + A′C + AC′D + A′C′D]′
1.1
2.2
3.3
4.4
The simplified SOP (Sum Of Product) form of the boolean expression (P + Q' + R') . (P + Q' + R) . (P + Q + R') is
1.(P'.Q + R')
2.(P + Q'.R')
3. (P'.Q + R)
4. (P.Q + R)
The switching expression corresponding to f(A, B, C, D) = Σ (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'
The total number of prime implicants of the function f(w, x, y, z) = Σ(0, 2, 4, 5, 6, 10) is ________.
1.2
2.3
3.4
4.5
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
We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is
1.1
2.2
3.4
4.5
What is the minimum number of NAND gates required to implement a 2-input EXCLUSIVE-OR function without using any other logic gate?
1.3
2.4
3.5
4.6
Which are the essential prime implicants of the following Boolean function? f(a, b, c) = a'c + ac' + b'c
1.a'c and ac'
2. a'c and b'c
3.a'c only
4.ac' and bc'
Which of the following expressions is equivalent to (A⊕B)⊕C
1.(A+B+C)(A¯+B¯+C¯)
2.(A+B+C)(A¯+B¯+C)
3.ABC+A¯(B⊕C)+B¯(A⊕C)
4.None of the above
Which of the following input sequences for a cross-coupled R-S flip-flop realized with two NAND gates may lead to an oscillation ?
1.11, 00
2. 01, 10
3. 10, 01
4. 00, 11
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