Logic gates and circuits

Question 1

Describe the function of the NOT gate.

Represent it in both logical and Boolean algebraic form

Answer 1

X is 1 if input A is 0. (Converts a high input to a low one and vise versa)

X = NOT A
X = ā

Question 2

Describe the function of the AND gate.

Represent it in both logical and Boolean algebraic form

Answer 2

X is 1 if A AND B are 1. (Gives a high output only if both inputs are high)

X = A AND B 
X = a . b

Question 3

Describe the function of the OR gate.

Represent it in both logical and Boolean algebraic form

Answer 3

X is 1 if A OR B is 1. (Gives a high output if at least one of the inputs is high)

X = A OR B 
X = a + b

Question 4

Draw the NOR gate and give its truth table.

Describe the function of the NOR gate.

Represent it in both logical and Boolean algebraic form

Answer 4

Truth table -- 
00 - 1 
01 - 0
10 - 0
11 - 0

X is 1 if A NOR B is 1. (Gives a high output when both the inputs are low)

X  = A NOR B 
X = a + b (bar)

Question 5

Draw the NAND gate and give its truth table.

Describe the function of the NAND gate.

Represent it in both logical and Boolean algebraic form

Answer 5

Truth table –

00 - 1
01 - 1
10 - 1
11 - 0

X is 1 if A AND B are NOT both 1. (Gives a high output when both inputs are not high at the same time)

X = A NAND B 
X = a . b (bar)

Question 6

Draw the XOR gate and give its truth table.

Describe the function of the XOR gate.

Represent it in both logical and Boolean algebraic form

Answer 6

Truth table –

00 - 0
01 - 1
10 - 1
11 - 0

X is 1 if (A is 1 and B is 0) or if (A is 0 and B is 1). (Gives a high output when the number of high inputs is not even)

X = A XOR B 
X = (a . b_) + (a_ . b)

Question 7

Draw a logic circuit and its truth table for the following scenario.

There are 3 inputs to he logic circuit representing key parameters in the chemical process. An alarm, X will give an output value of 1 depending on certain conditions in the chemical process. The following table describes the process conditions being monitored.

1. chemical reaction rate - R (input) - 0 (reaction rate <40 mol/l/sec) ; 1 (reaction rate is >= 40 mol/l/sec
2. process temperature - T - 0 (temperature > 115 d); 1 (temp. <= 115 d)
3. concentration of chemicals - C - 0 (concentration = 4 mol); 1 (concentration > 4 mol)

Logic statement -

X = 1 if R = 0 OR (C = 1 AND T = 0) OR (R = 1 AND T = 0)

Answer 7

Make sure that the statement is correct :

X = 1 if R is NOT 1 OR (C is 1 AND T is NOT 1) OR (R is 1 AND T is NOT 1)