Create a Logic-circuit for the given Logic statement and complete the Truth-table

Q1. a)  Draw the logic circuit represented by the logic statement.

X = 1, if (B is 0 AND S is 0) OR (P is 0 AND S is 1)

Solution :

⇒  Convert the logic statement in terms of 1's, like -

X = 1, if (B is NOT 1 AND S is NOT 1) OR (P is NOT 1 AND S is 1)

⇒  To draw the logic circit, we start with each part in brackets, starting from lower level from inside.

⇒  B is NOT 1 is one gate, means NOT of B, invert the signal B using NOT-gate.

Step-1 :  Join the NOT of B, and NOT of S, using AND-gate for the logic statement - (B is NOT 1 AND S is NOT 1).

Step-2 :  Similarly, join the NOT of P, and S, using AND-gate for the logic statement - (P is NOT 1 AND S is 1).

Step-3 :  Finally, join the logic statements of Step-1 and Step-2 using OR-gate.

b)  Complete the truth table for the above logic statement.

Group G1 = (B is 0 AND S is 0) =  B . S
Group G2 = (P is 0 AND S is 1) =  P . S
Output X = G1 OR G2 =  G1 + G2

Q2.  Draw a logic circuit for the given logic statement :

X = (A XOR B) AND (B OR NOT C)

Do not attempt to simplify the logic statement. All logic gates must have a maximum of two inputs.

Solution :

Step-1 :  Draw Logic-circuit for the inner first group of logic statements (A XOR B).

Step-2 :  Draw Logic-circuit for the inner second group of logic statements (B OR NOT C).

Step-3 :  Draw and join the two groups of logic circuits with AND gate.

Q3.  Consider the following logic statement :

X = (((A AND NOT B) OR (NOT (B NOR C))) AND C)

a)  Draw a logic circuit to represent the given logic statement.

Do not attempt to simplify the logic statement. All logic gates must have a maximum of two inputs.

Solution :

Step-1 :  Draw Logic-circuit for the first inner group for logic statements (B NOR C).

Step-2 :  Invert the output of first inner group by putting NOT-gate for logic statement (NOT (B NOR C)).

Step-3 :  Draw Logic-circuit for second inner group for logic statement (A AND NOT B).

Step-4 :  Draw and join the first two groups of logic circuits with OR gate for logic statement ((A AND NOT B) OR (NOT (B NOR C))).

Step-5 :  Join the output of Step-4 with input C using AND-gate to complete the logic statement for output X.

b)  Complete the truth table for the given logic statement.

Group G1 = (A AND NOT B) =  A . B
Group G2 = NOT (B NOR C) =  NOT (B + C) =  B + C
Group G3 = G1 OR G2 =  G1 + G2
Output X = G3 AND C
Output X =  G3 . C

Write a Logic statement for the given logic-circuit and complete the Truth-table

Q1.  Consider the logic circuit.

a)  Write a logic statement to match the given logic circuit.

Solution :

Step-1 :  Start writing the logic statement for each logic-gate from left hand side i.e. from input side to output side.

Step-2 :  A is 1 XOR C is 1,     B is 1 NAND C is NOT 1

Step-3 :  Join the both logic statement for each logic-gate using OR-gate to get the output X, like -

Logic statement :

X = 1, if (A is 1 XOR C is 1) OR (B is 1 NAND C is NOT 1)

X = 1, if (A XOR C) OR (B NAND NOT C)

b)  Complete the truth table for the given logic statement.

Group G1 = (A XOR C) =  A ⊕ C

Group G3 = B NAND C = NOT (B AND C) =   NOT  G2

Group G3 =  G2, where G2 =(B . C)

Output X = G1 OR G3 =  G1 + G3

Write a Logic expression for the given Truth-table and draw the Logic-circuit

Q1.  Consider the truth table.

a)  Write a logic expression for the given truth table.

Do not simplify the logic expression.

Solution :

Step-1 :  Identify the input conditions which produces the output X = 1 and write its logic-statement (as products of inputs).

Step-2 :  X=1, if (A is 1) AND (B is NOT 1) AND (C is NOT 1)

X=1, if (A is 1) AND (B is 1) AND (C is 1)

Step-3 :  Join the logic statements with logic operator "OR" (as sum of products), like -

Logic statement :

X = 1, if (A is 1 AND B is NOT 1 AND C is NOT 1) OR (A is 1 AND B is 1 AND C is 1)

X = ((A AND B AND C) OR (A AND NOT B AND NOT C))

b)  Draw a logic circuit to represent the given truth table.

Each logic gate should have maximum of two inputs.

Do not simplify the logic circuit.

Q2. a)  Write down a logic expression corresponding to the following truth table:

Solution :

Step-1 :  Identify the input conditions which produces the output X = 1 and write its logic-statement (as products of inputs).

Step-2 :  X=1, if (A is NOT 1) AND (B is NOT 1) AND (C is NOT 1)

X=1, if (A is NOT 1) AND (B is NOT 1) AND (C is 1)

X=1, if (A is 1) AND (B is NOT 1) AND (C is NOT 1)

X=1, if (A is 1) AND (B is NOT 1) AND (C is 1)

Step-3 :  Join the logic statements with logic operator "OR" (as sum of products), like -

Logic statement :

X = ((NOT A AND NOT B AND NOT C) OR (NOT A AND NOT B AND C) OR (A AND NOT B AND NOT C) OR (A AND NOT B AND C))

b)  Show that the following logic expression produces the same output as your answer to part a above:

X = (NOT A AND NOT B) OR (A AND NOT B)

Solution :

Input			Working		Output
A	B	C	G1 = A! . B!	G2 = A . B!	X = G1 + G2
0	0	0	1	0	1
0	0	1	1	0	1
0	1	0	0	0	0
0	1	1	0	0	0
1	0	0	0	1	1
1	0	1	0	1	1
1	1	0	0	0	0
1	1	1	0	0	0

Since the Truth-table of part a and part b is same, the output produced by logic expression of part b is the same as of part a.

Re-draw the Logic-circuit by replacing one or more logic-gates with specific logic-gates

Q1.  Consider the logic circuit.

a)  Redraw the logic circuit using only 4 logic gates. Each logic gate used must have a maximum of two inputs.

Solution :

Step-1 :  Replace NOT of OR-gate with NOR-gate.

Step-2 :  Replace NOT of AND-gate with NAND-gate.

b)  Complete the truth table for the given logic statement.

c)  Describe the purpose of a logic gate in a logic circuit.

⇒  To carry out a logical operation.

⇒  To control the flow of electricity through a logic circuit.

⇒  An input is given and the logic of the gate is applied to give an output.

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