Write the logic symbol and truth table of NAND gate.

In digital electronics, a NAND gate which is a negative-AND gate, is a logic gate which produces an output which is false only if all its inputs are true. Thus its output is complement to that of the AND gate.

How will you obtain OR, AND gates from the NAND and NOR gates? Write symbol, Boolean formula and truth table.

(i) To obtain AND gates from NAND gates: For obtaining AND gate from NAND gate the output of NAND gate is connected to the input (obtained from NAND gate by joining the two inputs).For obtaining OR gate from NAND gate the inputs \$A\$ and \$B\$ are connected to the two NOT gates obtained from NAND gates. The input get inverted as \$\overline { A }\$ and \$ \overline { B }\$. These inputs are then fed to the NAND gate as shown in fig. drawn below.Boolean formual: \$y=\overline { y } =\overline { \overline { A\cdot B } } =A\cdot B\$Input OutputA B y y01 01 0 0 1 1 1 1 1 0 0 0 0 1(ii) To obtain OR gate from NAND gate: For obtaining OR gate from NAND gate the input \$A\$ and \$B\$ are connected to the two NOT gates obtained from NAND gates. The input gate inverted as \$\overline { A }\$ and \$ \overline { B }\$. These inputs are then fed to the NAND gate as shown in fig, drawn belows.Boolean formula: \$ y=\overline { \overline { A } } \overline { \overline { B } } =\overline { \overline { A } } +\overline { \overline { B } } =A+B\$Input OutputA0 1 01 B0011 \$\overline { A }\$ 1 0 1 0\$ \overline { B }\$ 1 1 0 0 y 0 1 1 1(iii) To obtain OR gate from NOR gate: To obtain OR gate from NOR gate the inputs are connected to NOR gate which in turn is again connected to NOR gate.Input Output A \$\overline { A }\$ 0 1 1 0(iv) To obtain AND gate from NOR gate: To obtain AND gate from NOR gate the inputs are connected to NOT gate obtained from NOR gate giving inverted \$ A\left( \overline { A } \right) \$ and inverted \$B\left( \overline { B } \right)\$.Which is inturn are again connected is NOR gate.Boolean formula: \$ \overline { y } =\overline { A } +\overline { B } =\overline { \overline { A } +\overline { B } } =A\cdot B\$

Explain why NAND gate is known as universal gate.

NAND Gate is called Universal Gates because all the other gates (NOT, AND, OR and NOR)can be created by using this gate.

The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform.

From the figure we can see the logic gate table of NOT and NOR gate\$A\$ \$NOT \ gate(X)\$1 00 10 11 01 00 10 1\$B\$ \$NOT \ gate(Y)\$1 00 11 00 11 00 11 0\$X\$ \$Y\$ \$NOR \ gate\$0 0 11 1 01 0 00 1 00 0 11 1 0 1 0 0

Which logic gates is represented by the following combination of logic gates?

This is a case of AND gate. Input and output are shown below\$\therefore\$ \$y=\overline { \overline { A } +\overline { B } } =\overline { \overline { A } .\overline { B } } =AB\$ (since \$\overline { A } +\overline { B } =\overline { A } .\overline { B } \$)

The Boolean expression for NAND gate is -

The Boolean algebra for \${\text{AND}}\$ gate is-\$Y = A.B\$So, the Boolean algebra for \${\text{NAND}}\$ gate is-\$Y = \overline {A.B} \$

When all the inputs of a NAND gate are connected together, the resulting circuit is:

The equation of NAND gate is \$Y=\bar{A}.\bar{B}\$When both the terminals are connected together.\$A=B=A\$\$Y=\bar{A}.\bar{A} =\bar{A}. \bar{A}=\bar{A}\$Which is nothing but the equation of NOT gate.\$Y=\bar{A}\$Option \$\textbf A\$ is the correct answer

In the circuit below, \$A\$ and \$B\$ represent two inputs and \$C\$ represents the output. The circuit represents

Given, \$A\$ and \$B\$ are inputs and \$C\$ is output.Assume that some voltage is applied across \$AB,\$If the voltage is positive, then diode corresponding to \$A\$ will be on and the other diode will be off\$\Rightarrow C=A\$If the voltage is negative then diode corresponding to \$B\$ will be on and the other diode will be off\$\Rightarrow C=B\$Therefore we can say that \$C=A or B\$Therefore it acts like \$OR\$ gate.So the correct option is \$D.\$

To get output \$1\$ for the following circuit, the correct choice for the input is.

From left side the first gate is OR gate and next one is AND gate. So the out put of OR gate is \$A+B\$ and the output of AND gate \$Y=(A+B).C\$We know that for AND gate the put will be 1 if both inputs are 1. So, \$A+B =1 \$and \$C=1\$In logic gate , \$ 1+0=1\$ so \$A=1, B=0 , C=1 \$ will be the correct choice for output 1.

Basic Knowledge of Logic Gates: Basic Gates | Definition, Examples, Diagrams

example

Types of logic gates

Attached figure show different types of gates and Boolean functions of outputs.
Note:
Digital signals are denoted by 1 and 0 (or High and Low).

definition

Truth Table

Truth table is a table that lists all possible inputs and their corresponding outputs for a given digital circuit.
NOT gate:

Input	Output
0	1
1	0

OR Gate:

Input 1	Input 2	Output
0	0	0
0	1	1
1	0	1
1	1	1

AND gate:

Input 1	Input 2	Output
0	0	0
0	1	0
1	0	0
1	1	1

NOR gate:

Input 1	Input 2	Output
0	0	1
0	1	0
1	0	0
1	1	0

NAND gate:

Input 1	Input 2	Output
0	0	1
0	1	1
1	0	1
1	1	0

example

Combination of gates

To construct truth table of combination of gates, following steps are required:
1. Size of the truth table is given by

2^{n} \times n + m

where

n :

number of inputs and

m :

number of outputs
2. List down all possible combinations of inputs in the truth table.
3. For each input, find output of each logic gate and fill in the truth table according to its behaviour moving along with the direction of signals.

Consider the circuit given in the figure. Its truth table is given by:

A	B	C ( $= \overset{ˉ}{A}$ )	D ( $= B . C$ )	Q ( $= B + D$ )
0	0	1	0	0
0	1	1	1	1
1	0	0	0	0
1	1	0	0	1

definition

Universal Gates

NAND and NOR gates are called universal gates because any other gate can be derived with the use of combination of only NAND gates (or only NOR gates).
Construction of AND, OR and NOT gate using NAND gate is shown in the attached figure.

Basic Knowledge of Logic Gates: Basic Gates