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Question
Write the truth table for the circuit shown in figure. Name the gate that the circuit resembles.
Solution
This is ‘AND’ Gate and its characteristics are as follows:
(1) It has two inputs (A and B) and only one output (Y).
(2) Boolean expression us Y = A·B is read as "Y equals A AND B".
(3) Realization of AND gate
Logical symbol of AND gate
(i) A = 0, 8 = 0
The voltage supply through R is forward biasing diodes D1 and D2 (offers low resistance), the voltage V would drop across R. The output voltage at Y = the voltage across diode = 0
(ii) A = 0, B = 1
D1 = Conducts, D2 = Not Conducts
The out voltage at Y = The voltage across the diode (D1) = 0
(iii) A = 1, B = 0
D1 = Conducts, D2 = Not conducts
The out voltage at Y = The voltage across the diode (D2) = 0
(iv) A = 1, B = 1
None of the diode conducts
The out voltage at Y = Battery voltage = 1
(4) Truth table for ‘AND’ gate
| A | B | V0 = A · B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
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RELATED QUESTIONS
Which logic gate corresponds to the truth table given below?
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A |
B |
Y |
|
0 |
0 |
I |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.
Write the truth table for circuit given in figure below consisting of NOR gates and identify the logic operation (OR, AND, NOT) which this circuit is performing.
(Hint: A = 0, B = 1 then A and B inputs of second NOR gate will be 0 and hence Y=1. Similarly work out the values of Y for other combinations of A and B. Compare with the truth table of OR, AND, NOT gates and find the correct one.)
Answer the following question :
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The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.
Let \[X = A \overline{ BC} + B\overline{ CA} + C\overline{AB } .\] Evaluate X for A = B = C = 1.
With the help of a diagram, show how you can use several NAND gates to obtain an OR gate.
Useful Constants and Relations :
| 1. Speed of Light in Vacuum | (c) = 3.00 x 108 m/s |
| 2. Charge of a proton | (e) = 1.60 x 10-19C |
| 3. Planck's Constant | (h) = 6.6 x 10-34 Js |
| 4. Permeability of vacuum | (μ0) = 4π x 10-7 Hm-1 |
| 5. Electron Volt | (1eV ) = 1.6 x 10 |
| 6. Unified Atomic Mass Unit | (1u) = 931 MeV |
| (π) = 3.14 | |
| ( ln 2 ) = 0.693 |
The Boolean expression for NAND gate is
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