Test: Logic Gates - 2

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:
    
    

The given truth table matches with the NOR logic gate.

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:
    
    

The given truth table matches with the NAND logic gate.

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

CONCEPT:

• OR gate - The OR gate is defined as the gate in which if one of the inputs is true then the result will also true.
• AND gate - The AND gate is defined as the gate in which if one of the inputs is false then the result will also false.
• NOT gate - The NOT gate is defined as the output attains state 1 if and only if the input does not attain state 1.
• NOR gate - NOR gate is defined as it is the combination of NOT and OR gate.

CALCULATION:
Let us the different cases.
Case I - When A = 0, B = 0
The LED will glow.
Therefore, Y = 1
Case II - When A = 1, B = 0
The LED will not glow.
Therefore, Y = 0
Case III - When A = 0, B = 1
The LED will not glow.
Therefore, Y = 0
Case IV - When A = 1, B = 1
The LED will glow.
Therefore, Y = 0
The truth table is written as;

Here we see the results it will show the nature of NOR.
Hence, option 3) is the correct answer.

Concept:
Logic gates are:
1.AND Gate

2. NAND Gate

3. OR Gate

Calculation:
Output of combination of logic gates is given as


So the output y is high i.e., 1.
Hence, Output voltage is V0 = 5 V.

CONCEPT:

• Logic gate: The digital circuit that can be analysed 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.

NOR gate: It is a digital circuit having two or more inputs but only one output.
It gives a high output if either input A or B or both are low (0) otherwise it gives a high output (1).
It is described by the Boolean expression: 
The above logic gate is the NOR gate.

Truth table for NOR gate:

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.

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.

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

• The combination of AND gate and NOT gate gives the NAND gate.
• he Boolean algebra for AND gate is 

Therefore option 3 is correct.

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.

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

CONCEPT:

• Logic gate: The digital circuit that can be analysed 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.

Combination of Logic Gates

The above combination of the logic gate is the NAND gate.

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.
• There are primarily three logic gates namely the OR gate, the AND gate, and the NOT gate.

A logic gate has one or more inputs but only one output. Thus, option 2 is correct.
It is an electronic device that implements a Boolean function. Thus option 1 is correct.
A logic gate follows a logical relationship between input and output voltages. Thus option 3 is incorrect.

CONCEPT:

• 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:

• The high and low inputs correspond to 1 and 0 respectively.
• In a NOT gate, a low output is obtained from a high input and vice versa.
• Therefore, as inferred from the truth table of the NOT gate, it inverts the input signal.

Concept:
De Morgan’s law states that:



This is OR gate. So option 4 is correct.

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 work on the truth table.

AND Gate: The Logic AND Gate is a type of digital logic circuit whose output goes 1 (HIGH) only when all of its inputs are 1 (HIGH)

The truth table for AND gate:

• As the logic gates give only one output. It is not the continuous output giving element. But the fuse should work continuously. That's why the logic gates can’t be used as a fuse in an electric circuit. So statement 3 is wrong. So option 3 is correct.
• As the logic gates give only one output. It is not the continuous output giving element. In case of an on or off alarms, we just need only one output, either on or off. That's why the logic gates can be used to on or off the alarm. So statement 2 is correct.
• The logic gates work on the truth table as shown in the example on the concept part because it can give either yes or no as output. So statement 1 is correct.

CONCEPT:

• Logic gate: The digital circuit that can be analysed 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.

OR gate: It is a digital circuit having two or more inputs but only one output.
It gives a high output if either input A or B or both are high (1) otherwise it gives a low output (0).
It is described by the Boolean expression: A + B = Y
The above logic gate is the OR gate.
The truth table of OR gate: