EC401- DIGITAL ELECTRONICS TUTORIAL SHEET:5 1. A company has 4 directors A, B, C, and D. The percentage of shares held by them is 35%, 30%, 25%, and 10% respectively. There voting powers is proportional to shares held by them. Any major decision must have support of 60% or above of the stock. Design a combination logic circuit for voting in the company. 2. Design a combinational circuit that detects an error in the representation of a decimal digit in BCD. In other words, obtain a logic diagram whose output is logic-1 when the inputs contain an unused combination in the code.
3. Design a combinational circuit with four input lines that represent a decimal digit in BCD and four output lines that tha t generates the 9’s complement of the the input digit. Hint: Find the truth table with input side as BCD input and output side as 9’s complement of the same. 4. Design a combinational circuit whose input is a four-bit number and whose output is the 2’s complement complement of the input number. 5. Design a combinational circuit that multiplies by 5 an input decimal digit represented in BCD. The output is also in BCD. Show that the outputs can be obtained from the input lines without using an y logic gates. 6. Implement the four Boolean functions using three half-adder circuits. D= AθBθC, where θ is XOR gate. E= A’BC +AB’C F= ABC’ + (A’ + B’) C G= ABC 7. Realize 2 bit magnitude comparator, using one bit comparator as black box, which is having two inputs A and B, each of 2 bits, and produces three outputs G, L and E for A>B, A
Using : (a) 2:4 decoders and some basic gates only (b) 2 x1 Multiplexers only 12. Realize the F(x1, x2, x3, x4) = m(0,1,2,3,4,9,13,14,15) using 8X1 Mux. 13. Implement the following Boolean function using 8X1 Mux, with A, B & D connected to selection lines S2, S1, S0 respectively. F(A,B,C,D)=m(0,1,4,6,12,13). 14. Realize following function F(A,B,C)=AB’ +ABC +A’B’C, by using minimum number of Multiplexers (a) 2x1 MUX (b) 4x1 MUX (c) 8x1 MUX 15. Realize the function f (B, A, C) = ∑ m (2, 3, 5, 6) using a 4x1 Multiplexers. Note that f (B, A, C) is given instead of f (A, B, C).
16. What is the logic function of the MUX circuit shown below:
17. The circuit shown below uses three 2x1 Multiplexers. Determine the truth table of Z, given by the circuit assuming that when S=0, Output of Mux is I1and when S=1, Output of Mux is I2.
I(3)
I(1) Y
I(2)
I(2)
S(2) I(1) Y
I2
I(1)
S0
I(1) Y
I(0)
I2
S1
18. Realize the following truth table using 4X1 Multiplexer. A 0 0 0 0 1 1 1 1
B 0 0 1 1 0 0 1 1
C 0 1 0 1 0 1 0 1
F 0 0 0 1 0 1 1 1
19. Realize full Subtractor using 4x1 Multiplexers and basic logic gates.
20. Design a Binary to Gray code Converter circuit using 4X1Multiplexers. Inputs are of 4 bit binary number. 21. A function G has been realized with 2:1 multiplexers and some additional gates as shown in the figure below.
a. Express G as a standard sum of products b. Implement the same function using an 8:1 Multiplexer. 22. Consider the following circuit.
In the above circuit, S2 to S0 are select lines and X7 to X0 are input lines. S0 and X0 are LSBs. What is the output Y?
