Thursday, November 13, 2014

Previous GATE Questions on Combinational Circuits with Solutions (1987 - Till Date)


1.       Indicate which of the following logic gates can be used to realized all possible combinational logic functions :
        a.       OR gates only
        b.      NAND gates only
        c.       EX-OR gates only
        d.      NOR gates only
Answer:      B & D
                             Solution :


1.       The number of Boolean functions that can be generated by n variables is equal to :

Answer:      B
                Solution :

2.       The minimal function that can detect a “divisible by 3” 8421 BCD code digit (representation is D8D4D2D1) is given by
Answer:     B
               Solution :


1.       A combinational circuit has three inputs A, B and C and an output F. F is true only for the following combinations.

A is false and B is true
A is false and C is true
A, B and C are all false
A, B and C are all true
        a.       Write the truth table for F. Use convention, true = 1 and false = 0.
        b.      Write the simplified expression for F as a sum of products.
        c.       Write the simplified expression for F as a product of sums.
        d.      Draw the logic circuit implementation of F using the minimum number of 2 input                    NAND gates only.


1.       Signals A, B, C, D and D’ are available. Using a single 8 to 1 multiplexer and no other gate, implement the Boolean function F(A, B,C, D) = BC + ABD’ + A’C’D


1.       The carry look ahead adder is a parallel carry adder where all sum digits are generated directly from the input digits.  [TRUE / FALSE]
Answer:    TRUE 

2.   A Boolean function, F is given as sum of product (SOP) terms as P = m (3, 4, 5, 6) with A, B and C as inputs. The function, F can be expressed on the karnaugh’s map shown below.
        a.       Implement this function on an 8:1 MUX
        b.      What will be the minimized SOP expression for F2.


1.   A ‘code converter’ is to be designed to convert from the BCD (5421) code to normal BCD (8421) code. The input BCD combinations for each digit are given below. A block diagram of the converter is shown in figure.
        a.       Draw K- map for outputs W, X, Y and Z
        b.      Obtain minimized expression for the outputs W, X, Y and Z


1.       A two bit binary multiplier can be implemented using
        a.       2 input AND gates only
        b.      2 input XOR gates and 2 input AND gates only
        c.       Two  2 input NOR gates and one XOR gate
        d.      XOR gates and shift registers

Answer:      B
                  Solution : 


1.       For a binary half – subtractor having two inputs A and B, the correct set of logical expressions for the outputs D (= A minus B) and X (= borrow) are
Answer:       C
                 Solution :

2.   In a certain application, four inputs A, B, C, D (both true and complement forms available) are fed to logic circuit, producing an output F which operates a relay. The relay turns on when F(ABCD) = 1 for the following states of the inputs (ABCD): ‘0000’, ‘0010’, ‘0101’, ‘0110’, ‘1101’ and ‘1110’. States ‘1000’ and ‘1001’ do not occur, and for the remaining states, the relay is off. Minimize F with the help of a Karnaugh map and realize it using a minimum number of 3 input NAND gates.

                 Solution :   



 1.   The operating conditions (ON = 1 and OFF = 0) of three pumps (x, y, z) are to be monitored, x = 1 implies that pump x is on. It is required that the indicator (LED) on the panel should glow when a majority of the pumps fail.
a.        Enter the logical values in the K map in the format shown in figure. Derive the minimal    
Boolean sum of products expression whose output is zero when a majority of the pumps fail.
b.       The above expression is implemented using logic gates, and point P is the output of the
circuit, as shown in given figure, P is at 0 volts when a majority of the pumps fails and is at 5 volts otherwise. Design a circuit to derive the LED using this output.
The current through the LED should be 10 mA and the voltage drop across it is 1 volt. Assume that P can source or sink 10 mA and a 5 volts supply is available.

                 Solution :

2.   A one bit full adder is to be implemented using 8 to 1 multiplexers (MUX).
        a.       Write the truth table for sum (S) and carry to the next stage (CN), in terms of the two bits (A, B) and the carry from the previous stage (CP). The truth table should be in the   ascending order of (A, B, CP) i.e. (000, 001, 010..... etc).
        b.      Implement S and CN using 8 to 1 multiplexers.
                 Solution :


1.       For the ring oscillator shown in the figure, the propagation delay of each inverter is 100 pico sec. What is the fundamental frequency of the oscillator output?
        a.       10 MHz
        b.      100 MHz
        c.       1 GHz
        d.      2 GHz
Answer:     C
           Solution :     

2.       In the figure, the LED
        a.       Emits light when both S1 and S2 are closed.
        b.      Emits light when both S1 and S2 are open.
        c.       Emits light when only of S1 or S2 is closed.
        d.      Does not emit light, irrespective of the switch positions.
Answer:     D
           Solution : 

     3.   For the digital block shown in the figure, the output Y = f(S3,S2,S2,S0), where S3 is MSB and S0 is  LSB. Y is given in terms of minterms as Y = Σm(1,5,6,7,11,12,13,15) and its complement is given as Σm(0,2,3,4,8,9,10,14).
        a.       Enter the logical values in the given Karnaugh map in the figure, for the output Y.
        b.      Write down the expression for Y in sum of products form using minimum number of   terms.
        c.       Draw the circuit for the digital logic boxes using four 2 input NAND gates only for    each of the boxes.

           Solution :  


1.        If the inputs X3, X2, X1, X0 to the ROM in the figure are 8-4-2-1 BCD numbers, then the outputs Y3Y2Y1Y0 are

        a.       Gary code numbers
        b.      2-4-2-1 BCD numbers
        c.       Excess-3 code numbers
        d.      None of the above
Answer:     B
                 Solution : 


1.       The circuit shown in the figure has 4 boxes each described by inputs P,Q,R and outputs Y, Z with the following relation.
      The circuit acts as a
        a.       4 bit adder giving P + Q
        b.      4 bit subtractor giving P – Q
        c.       4 bit subtractor giving Q – P
        d.      4 bit adder giving P + Q + R

Answer:      B
                   Solution :
2.   The circuit shown in the figure converts
        a.       BCD to Binary code
        b.      Binary to Excess – 3 code
        c.       Excess – 3 code to Gray code
        d.      Gray to Binary code

Answer:      A
                   Solution :


1.   A Boolean function f of two variables x and y is defined as follows:

f(0,0) = f(0,1) = f(1,0) = 1; and f(1,0) = 0
Assuming complements of x and y are not available, a minimum cost solution for realizing f using only 2 input NOR gates and 2 input OR gates (each having unit cost) would have a total cost of
        a.       1 unit
        b.      4 units
        c.       3 unit
        d.      2 units
Answer:     D
                 Solution :

      3.       A digital system is required to amplify a binary encoded audio signal. The user should be able to control  the gain of the amplifier from a minimum to a maximum in 100 increments. The minimum number of bits required to encode in straight binary is
             a.       8
             b.      6
             c.       5
             d.      7
Answer:     D
                  Solution :


1.       The point P in the following figure is stuck-at-1. The output f will be
Answer:     D
               Solution :  


Statement for linked answer questions: 1 & 2
Two products are sold from a vending machine, which has two push buttons P1 and P2. When a button is pressed, the price of the corresponding product is displayed in a 7-segment display.
If no buttons are pressed, ‘0’ is displayed, signifying ‘Rs. 0’.
If only P1 is pressed, ‘2’ is displayed, signifying ‘Rs. 2’.
If only P2 is pressed, ‘5’ is displayed, signifying ‘Rs. 5’.
If both P1 and P2 are pressed, ‘E’ is displayed, signifying ‘Error’.
The names of the segments in the 7-segment display, and the glow of the display for ‘0’, ‘2’, ‘5’ and ‘E’ are shown below.
            (i)                  Push button pressed / not pressed is equivalent to logic 1 / 0 respectively
            (ii)                A segment glowing / not glowing in the display is equivalent to logic 1 / 0 respectively

1.       If segments a to g are considered as functions of P1 and P2, then which of the following is correct?
Answer:     B
2.       What are the minimum numbers of NOT gates and 2-inout OR gates required to design the logic of the driver for this 7-segment display?
        a.       3 NOT and 4 OR 
        b.      2 NOT and 4 OR
        c.       1 NOT and 3 OR
        d.      2 NOT and 3 OR
Answer:     D
                Solution (6 & 7) :

1.       In the circuit shown, the device connected to Y5 can have address in the range

        a.       2000 – 20FF
        b.      2D00 – 2DFF
        c.       2E00 – 2EFF
        d.      FD00 – FDFF
Answer:     B
               Solution :


1.       The output Y of a 2-bit comparator is logic 1 whenever the 2 bit input A is greater than the 2 bit input B. The number of combinations for which the output is logic 1, is
          a.       4
          b.      6
          c.       8
          d.      10
Answer:     B
                 Solution :


1.       A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles
        a.       An AND gate
        b.      An OR gate
        c.       An XOR gate
        d.      A NAND gate
Answer:     C
               Solution :

2.       In the circuit shown below, Q1 has negligible collector to emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If VCC is +5 volts, X and Y are digital signals with 0 volts as logic 0 and VCC as logic 1, then the Boolean expression for Z is
  Answer:     B
                Solution :


1.       For an n – variable Boolean function, the maximum number of prime implicants is
        a.       2(n – 1)    
        b.      n/2
        c.       2n
        d.      2(n – 1) 
Answer:     D
                Solution :

2.       In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X – Y) are given by 
              Answer:     C
                Solution :

3.   A 16 bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure. The carry propagation delay of each FA is 12 ns and the sum propagation delay of each FA is 15 ns. The worst case delay (in ns) of this 16 – bit adder will be…………

Answer:     195
                 Solution :

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