Logic Gates Test - 1

The correct answer is NOR gate.

Concept:

• A Universal Gate is a gate by which every other gate can be realized.
• AND, OR, NOT, etc. are basic gates.
• NAND, NOR  are the universal gate.

Example:

NOT, AND and OR gate realization using NAND gate is as shown:

Concept:

OR gate: If any of the input is high, it produces a high output.

The Boolean algebra for OR gate is X = A + B

Analysis:

A = 1, B = 1

X = 1 + 1 = 1

AND Gate: If both the inputs are high, it produces a high output.

The Boolean algebra for AND gate is X = A. B

NOT gate: It inverts the input. Whatever the input is given, it changes its value at the output.

The Boolean algebra for NOT gate is X = X̅

The correct answer is option 1) i.e. NOR

CONCEPT:

• Truth table: A truth table is a mathematical table used to represent the output of a given function based on the combination of input variables.
  • A truth table has two columns: the first column shows the combination of input variables and the last column shows the final output for each input.
• Logic gate: Logic gates are the basic building blocks of a digital system.
  • ​A logic gate works on the principle of a Boolean function which is a logical operation performed using one or more binary inputs that produce a single binary output.
  • The boolean function uses only two variables - zero or one.
  • The relationship between these inputs and the output is based on a certain logic. Based on this, logic gates are given names.
  • A few logic gates along with their symbol and truth table are as follows:

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EXPLANATION:

The given truth table matches with the NOR logic gate.

Additional Information

• The NOR gate is obtained by connecting the two basic logic gates - the OR gate and the NOT gate in series.

CONCEPT:

• The branch of algebra which deals with the values of the variables in the form of the truth values true and false is called Boolean algebra.
• True and false are usually denoted by 1 and 0 respectively.

EXPLANATION:

\(\bar C = \overline {A\;A} = \bar A\)

\(\bar D = \overline {B\;B} = \bar B\)

\(Y = \overline {\bar A\;\bar B} = \overline {\bar A} + \overline {\bar B} = A + B\)

This is OR gate. So option 4 is correct.

CONCEPT

Logic gates: 

• It is an electric circuit, which works on simple Boolean algebra to perform a logical operation for one or more binary inputs that produce a single binary output.

Types of Logic gates:

AND Gate: If both the inputs are high, it produces a high output.

• The Boolean algebra for AND gate is X = A. B

OR gate: If any of the input is high, it produces a high output.

• The Boolean algebra for OR gate is X = A + B

NOT gate: It inverts the input. Whatever the input is given, it changes its value at the output.

• The Boolean algebra for NOT gate is X = X̅

EXPLANATION:

• In AND gate the output is 1 only when both the input is 1.
• So, If the output is 1 then,

A = 1 and B = 1.

• Hence, option 1 is correct.

CONCEPT:

• The branch of algebra that deals with the values of the variables in the form of the truth values i.e., true and false are called Boolean algebra.
• True and false are usually denoted by 1 and 0 respectively.

EXPLANATION:

Given that:

A = 1

B = 0

∴ B̅ = 1 (Since B̅ is reverse of B)

A + B̅ = 1 + 1 = 1 (Since A + A = A)

A + B̅ = 1 = A

CONCEPT:

• Logic gate: The digital circuit that can be analyzed with the help of Boolean algebra is called a logic gate or logic circuit.
• A logic gate has two or more inputs but only one output.

EXPLANATION:

• NAND gate: It a combination of an AND and a NOT gate.
  
• It is obtained by connecting the output fo an AND gate to the input of a NOT gate.
• It is described by the Boolean expression: \(Y = \overline {A \cdot B}\)
• The above logic gate is the NAND gate.
• The truth table of NAND gate:

Concept:

• A universal gate is a gate which can implement any Boolean function without need to use any other gate type.
• The NAND and NOR gates are universal gates.
• That means we can implement any logic function using NAND and NOR gates without need of AND, OR or NOT gates.
• NOR gate is formed by connecting a NOT gate at the output of OR gate.
• NAND gate is formed by connecting NOT gate the output of AND gate.

Truth Table of NOR gate is given:

The output of NOR gate is high when all inputs are low.

Explanation:

• As we see the truth table for NOR gate :
• When both the input is low (0), then output is high (1).
• As one input is low (0) and another input is high (1) or vice-versa, then output is low (0).
• When both the input is high (1), then output is low (0).

So when the output of NOR gate is high if all inputs are low.

CONCEPT:

• Logic gate: The digital circuit that can be analyzed with the help of Boolean algebra is called a logic gate or logic circuit.
• A logic gate has two or more inputs but only one output.
• Logic gates works on the ruth table.

EXPLANATION:

• When both the input signals A and B of NOR & NAND gate are connected together, we have one common input connection hence the resultant output will be NOT gated.
• As shown when both the inputs are combined in either NAND or NOR gate, they both will behave like a NOT gate

This will be the truth table for both NAND and NOR logic gate when their inputs are connected.

From the given circuit we can see that,

• Two Keys are connected parallel to a LED and a resistor.
• Hence if any of the keys is open, no current will flow through keys and hence bulb will glow
• But if both the keys are closed current will start flowing from keys instead of LEDs, since current (I) will always flow where resistance is minimum.
• Which means the truth table for the given circuit can be given as
• Here 1 shows key is closed and current can flows through it
• And 0 shows key is open and current can’t flow through it