CS 147 Practice Problems 3.
The following questions are practice problems associated with the lecture material on the
subject of Decoders and Multiplexers.
1.
2.Given the function f(W, X, Y, Z) = (Sigma)m(2, 3, 4, 6, 7, 15) + (Sigma)d(0, 5, 12,
13) and its K-map, is it possible to realize it using a single 4 --> 1 MUX by choosing
S1 S0 = W X, Di (a member of) {0, 1, Y, not Y, Z, not Z} ; i = 0, 1, 2, 3 (the
complements of the input variables are available). If your answer is positive show the
realiziation; if it's negative explain why.
3. . Implement the sum function for an adder using a 4-input-1-output multiplexer and an
inverter. Remember that the inputs for that function are A, B, and CI and the output is
simply S.
4.Simplify the following Boolean function by K-map
f(x,y,z) = m(0,2,4) + d(1,3)
5. You are to design a circuit that has two data inputs (A and B) and three control outputs
(C0,C1, and C2). The circuit should implement the function F specified in the function
truth table below. Please give the Boolean equation for F, and then show how to
implement this by PLA with 5 inputs and 1 output.
6.Given the expression
7 Construct a 2-bit counter with a sequence of states 00, 01, 11, and 10 using D flip-flops
and NAND gates
8.You have invented a new type of flip-flop that you have called MY flip-flop. The two
inputs are M and Y, the outputs are Q and Q'. The truth table of your flip-flop is given
below.
MY
Q+
00
0
01
Q
10
Q'
11
1
a.
b.
c.
d.
Give the characteristic equation of the new flip-flop.
Give the excitation table for the new flip-flop.
Show how to implement a T flip-flop using the new MY flip-flop.
Show how to implement your new MY flip-flop using a SR flip-flop. Give the
logic diagram (showing the SR flip-flop and logic gates
e. Give the gate level schematic of the new MY flip-flop (designed in section d
above), assuming that the SR flip-flop is a master-slave flip-flop
9. What type of FF can be used as an R-S, a T, or a D FF?
Q.1 What will be the output of Q if J is HIGH, PS and CLR are HIGH, and
the
clock
is
going
negative?
Q.2 Assume that K goes HIGH and J goes LOW; when will the FF reset?
Q.3 What logic levels must exist for the FF to be toggled by the clock?
Q.4 What two inputs to a J-K FF will override the other inputs?
Q.5 How is the J-K FF affected if PS and CLR are both LOW?
10. Give the circuit symbol ,the excitation table and the characteristic equation of each of the following flipflops:
R-S flip-flop.
D flip-flop.
J-K flip-flop.
T flip-flop.
11. A set dominate flip-flop has a set and a reset input. It differs from a conventional R-S flip-flop in that an
attempt to
simultaneously set and reset results in setting the flip-flop.
Obtain the characteristic table and characteristic equation for such a flip-flop.
Obtain a logic diagram for an asynchronous set-dominate flip-flop.
12. Beginning with an R-S flip-flop show how to get
D flip-flop.
J-K flip-flop.
T flip-flop.
13. Beginning with an D flip-flop show how to get
J-K flip-flop.
T flip-flop.
14. Beginning with an J-K flip-flop show how to get
D flip-flop.
T flip-flop.
15. Beginning with an T flip-flop show how to get
D flip-flop.
J-K flip-flop.
16.Implement a new flip-flop type, called X-Y flip-flop, that has the following truth table
X Y Q(t+1)
0 0 Reset
0 1 Q(t)
1 0 Q'(t)
1 1 Set