physics_logicLogic Gates Logic Gate: A gate is a digital circuit that follows curtain logical relationship between the input and output voltages. They are known as logic gates because they control the flow of information. 1. NOT GateThis is the most basic gate, with one input and one output. It produces a "1" output if the input is "0" and vice-versa. It produces an inverted version of the input at its output. This is why it is also knownas an inverter. Boolean Expression : ( Q = NOT A ).
 Input Output A Y 1 0 0 1
2. OR GateAn OR gate has two or more inputs with one output. Boolean Expression: ( Q = A or B ).
 INPUT INPUT OUTPUT A B Y 0 0 0 0 1 1 1 0 1 1 1 1
3. AND GateAn AND gate has two or more inputs with one output. Boolean Expression: AND gate is written as Q=A.B or Q=AB.Q=A AND B
 INPUT INPUT OUTPUT A B Y 0 0 0 0 1 0 1 0 0 1 1 1
4. NAND GateAn NAND gate has two or more inputs with one output. It is AND gate followed by NOT gate.NAND gates are called Universal Gates since by using these gates you can realise other basic gates like OR, AND and NOT.Boolean Expression of: ( Q = NOT(A AND B) ).
 INPUT INPUT OUTPUT A B Y 0 0 1 0 1 1 1 0 1 1 1 0
5. NOR GateAn NOR gate has two or more inputs with one output. It is NOT operator applied after OR gate.NOR gates are considered as universal gates because you can obtain all the gates like AND, OR, NOT by using only NOR gates
 INPUT INPUT OUTPUT A B Y 0 0 1 0 1 0 1 0 0 1 1 0
Boolean Notation for logic function
 Logic Function Boolean Notation AND A.B OR A+B NOT ⏨A$\overline{A}$ NAND ⏨⏨⏨A.B $\overline{A.B\phantom{\rule{0.22em}{0ex}}}$ NOR ⏨⏨⏨A+B $\overline{A+B\phantom{\rule{0.22em}{0ex}}}$
DeMorgan's Theorem in Logic Gates$\begin{array}{l}\overline{A.B}=\overline{A\phantom{\rule{0.22em}{0ex}}}+\overline{\phantom{\rule{0.22em}{0ex}}B\phantom{\rule{0.22em}{0ex}}}\\ \\ \overline{A+B}=\overline{A\phantom{\rule{0.22em}{0ex}}}.\overline{\phantom{\rule{0.22em}{0ex}}B\phantom{\rule{0.22em}{0ex}}}\phantom{\rule{0.44em}{0ex}}\\ \end{array}$ Q.14.18Write the truth table for circuit given in Fig. 14.47 below consisting of NOR gates and identify the logic operation (OR, AND, NOT) which this circuit is performing.
A.14.18$Q=\overline{A+B}$$=\overline{A\phantom{\rule{0.22em}{0ex}}}.\overline{\phantom{\rule{0.22em}{0ex}}B\phantom{\rule{0.22em}{0ex}}}$ Truth table
 A$A$ B$B$ ⏨A$\overline{A}$ ⏨⏨ B $\overline{\phantom{\rule{0.22em}{0ex}}B\phantom{\rule{0.22em}{0ex}}}$ C=⏨A.⏨⏨ B $C=\overline{A}.\overline{\phantom{\rule{0.22em}{0ex}}B\phantom{\rule{0.22em}{0ex}}}$ Y=⏨⏨⏨C+C=⏨C.⏨C=⏨C $Y=\overline{C+C}=\overline{C}.\overline{C}=\overline{C}\phantom{\rule{0.22em}{0ex}}$ 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1
So this is OR gate Q.14.19Write the truth table for the circuits given below consisting of NOR gates only. Identify the logic operations (OR, AND, NOT) performed by the two circuits.
A.14.19Circuit-1$Y=\overline{A+A}=\overline{A}.\overline{A}=\overline{A}\phantom{\rule{0.22em}{0ex}}$Truth table
 A Y 1 0 0 1
So this is NOR gate Circuit-2$\begin{array}{l}Q=\overline{A+A}=\overline{A}.\overline{A}=\overline{A}\phantom{\rule{0.22em}{0ex}}\\ \\ \overline{\overline{A}+\overline{B}}=\overline{\phantom{\rule{0.22em}{0ex}}\overline{A}\phantom{\rule{0.22em}{0ex}}}.\overline{\phantom{\rule{0.22em}{0ex}}\overline{B\phantom{\rule{0.22em}{0ex}}}\phantom{\rule{0.22em}{0ex}}}\end{array}$ Truth table
 A$A$ B$B$ ⏨A$\overline{A}$ ⏨⏨ B $\overline{\phantom{\rule{0.22em}{0ex}}B\phantom{\rule{0.22em}{0ex}}}$ ⏨⏨ ⏨A $\overline{\phantom{\rule{0.22em}{0ex}}\overline{A}\phantom{\rule{0.22em}{0ex}}}$ ⏨⏨ ⏨B $\overline{\phantom{\rule{0.22em}{0ex}}\overline{B}\phantom{\rule{0.22em}{0ex}}}$ Y=⏨⏨ ⏨A .⏨⏨ ⏨B =A.B$Y=\overline{\phantom{\rule{0.22em}{0ex}}\overline{A}\phantom{\rule{0.22em}{0ex}}}.\overline{\phantom{\rule{0.22em}{0ex}}\overline{B\phantom{\rule{0.22em}{0ex}}}\phantom{\rule{0.22em}{0ex}}}=A.B$ 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1
So this is AND gate