A circuit has four inputs p,q,r,s representing the natural binary number 0000=0,to 1111=15 p is the most significant bit .the circuit has one output, x,which is true if the input to the circuit represent is a prime number and false other wise (A) design a true table for this circuit, and hence obtain an expression for x in terms of P,Q,R,S.
A circuit has four inputs p,q,r,s representing the natural binary number 0000=0,to 1111=15 p is the most significant bit .the circuit has one output, x,which is true if the input to the circuit represent is a prime number and false other wise (A) design a true table for this circuit, and hence obtain an expression for x in terms of P,Q,R,S.
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A circuit has four inputs p,q,r,s representing the natural binary number 0000=0,to 1111=15 p is the most significant bit .the circuit has one output, x,which is true if the input to the circuit represent is a prime number and false other wise (A) design a true table for this circuit, and hence obtain an expression for x in terms of P,Q,R,S.
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Q3. A circuit has four inputs P,Q,R,S, representing the natural binary number 0000=0, to
1111=15. P is the most significant bit. The circuit has one output, X, which is true if the input to the
circuit represents is a prime number and false otherwise (A prime number is a number which is only
divisible by 1 and by itself. Note that zero (0000) and one (0001) are not considered as prime numbers)
a) Draw the truth table to represent the problem and obtain the function F as a Sum of
minterm.
b) Use the Karnaugh map to obtain a simplified expression for the function F.
c) Construct the circuit to implements the function using NOR gates only.
SECTION B: SEQUENTIAL CIRCUITS
Q4. Study the following state diagram carefully where X is the input, Y is the output and AB
are the states variables.
1/0
01
1/0
0/0
0/0
?
0/0
00
0/0
1/1
11
5
(a) Develop the state table with present state, ck-input, next state and input to flip flop (JK)
(b) Develop the sequential logic circuit
Q5. A sequential circuit whose specification is given in the state diagram below.
1/0
0/0
1/1
&
0/0
1/1
0/0
0/0
1/1
1/0
1/0
1/1
0/0
10
0/0
0/0
nminst
Devel
(a)
(
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Developed:
(a) The state table of from the state diagram.
0
(b) The state-reduction table.
(c) Redraw the state-reduction diagram.
(d) Assign 3 bits binary codes to the reduced states and treat the unused states as don't cares.
(e) Implement the sequential circuit using JK flip flops.
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Q6. Design a four bits Binary Coded Decimal counter using T flip flops going through
the states in the reverse order and treat the unused states as don't cares.
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X = 1 = Print number
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