Chapter 26 Valve & Digital Electronic 2 free study material by TEACHING CARE online tuition and coaching classes
Voltage Signal and Binary System.
- Voltage signal
The signal which represents the continuous variation of voltage with time is known as analogue voltage signal
The signal which has only two values. i.e. either a constant high value of voltage or zero value is called digital voltage signal
+ V_{0}
– V_{0}
Time
+V
O
Time
- Binary system
- A number system which has only two digits e. 0 (Low value) and 1 (High value) is known as binary system
- The electrical circuit which operates only in these two state e. 1 (On or High) and 0 (i.e. Off or Low) are known as digital circuits.
- Different names for the two states of digital signals :
State Code Name for the State | ||||||||
1 | On | Up | Closed | Excited | True | Pulse | High | Yes |
0 | Off | Down | Open | Unexcited | False | No pulse | Low | No |
Boolean Algebra.
- In Boolean algebra only two states of variables (0 and 1) are
- The variables (A, B, C ….) of Boolean Algebra are subjected to three
- Basic Boolean postulates and laws
- Boolean Postulates : 0 + A = A, 1 A = A, 1 + A = 1, 0 · A = 0,
- Identity law : A + A = A, A A = A
A + A = 1
- Negation law : A = A
- Commutative law : A + B = B + A, A B = B · A
- Associative law : (A+B) + C = A + (B+C), (A B) · C = A · (B · C)
- Distributive law : A (B+C) = A · B + A · C
- De Morgan’s laws :
A + B = A × B
and
A × B = A + B
also
A + AB = A + B
and
A(A + B) = AB
Logic Gates and Truth Table.
- Logic gate : The digital circuit that can be analysed with the help of Boolean algebra is called logic gate or logic 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.
- Truth table : The operation of a logic gate or circuit can be represented in a table which contains all possible inputs and their corresponding outputs is called the truth To write the truth table we use binary digits 1 and 0.
Different Logic Gates.
- The ‘OR’ gate
- It has two inputs (A and B) and only one output (Y)
- Boolean expression is Y = A + B
- Truth table and logic symbol
- The ‘AND’ gate
- It has two inputs and one
- Boolean expression is Y = A B
- Truth table and logic symbol :
A | B | Y = A · B |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
- The ‘NOT’ gate
- It has only one input and only one output
- Boolean expression is Y = A
- Truth table and logic symbol :
A | Y | = |
A |
0 | 1 | ||
1 | 0 |
Combination of Logic Gates.
- The ‘NAND’ gate : From ‘AND’ and ‘NOT’ gate
Boolean expression and truth table : Y = A × B
A | B | Y¢ | = A | × | B | Y |
0 | 0 | 0 | 1 | |||
0 | 1 | 0 | 1 | |||
1 | 0 | 0 | 1 | |||
1 | 1 | 1 | 0 |
- The ‘NOR’ gate : From ‘OR’ and ‘NOT’ gate
Boolean expression and truth table : Y = A + B
A | B | Y¢ | = | A | + | B | Y |
0 | 0 | 0 | 1 | ||||
0 | 1 | 1 | 0 | ||||
1 | 0 | 1 | 0 | ||||
1 | 1 | 1 | 0 |
- The ‘XOR’ gate : From ‘NOT’, ‘AND’ and ‘OR’ Known as exclusive OR gate.
or
The logic gate which gives high output (i.e., 1) if either input A or input B but not both are high (i.e. 1) is called exclusive OR gate or the XOR gate.
It may be noted that if both the inputs of the XOR gate are high, then the output is low (i.e., 0).
Boolean expression and truth table : Y = A Å B = AB + AB
A | B | Y |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
- The exclusive nor (XNOR) gate : XOR + NOT XNOR
Boolean expression : Y = A ¤ B =
Logic Gates Using ‘NAND’ Gate.
A B + AB
The NAND gate is the building block of the digital electronics. All the logic gates like the OR, the AND and the NOT can be constructed from the NAND gates.
- Construction of the ‘ NOT’ gate from the ‘ NAND’ gate
- When both the inputs (A and B) of the NAND gate are joined together then it works as the NOT
- Truth table and logic symbol
- Construction of the ‘AND’ gate from the ‘ NAND’
- When the output of the NAND gate is given to the input of the NOT gate (made from the NAND gate), then the resultant logic gate works as the AND gate
- Truth table and logic symbol
- Construction of the ‘ OR’ gate by the ‘NAND’ gate
- When the outputs of two NOT gates (obtained from the NAND gate) is given to the inputs of the NAND gate, the resultant logic gate works as the OR gate
- Truth table and logic symbol