## Unit – IV |

## Digital Electronics and Logic Circuit:

1. George Boole, a mathematician, developed Boolean algebra based on the science of logic. In 1938, a scientist called Shenon developed electrical circuits based on the Boolean algebra which are known as logic circuits.

2. In amplifier or oscillator circuits, the current or the voltage continuously change with time from minimum to maximum. Such a signal is called analog signal.

3. In calculators and computers, the voltage or the current has only two values, the maximum value indicated by ‘1’ and the minimum by ‘0’. Such a signal is known as a digital signal.

4. The number system which has only two symbols (either 0 or 1) is called binary number system. The circuit which handles binary voltage levels is called digital circuit.

5. There are two types of systems adopted for a logic circuit.

a) Positive Logic System:

In this type of system, the higher positive voltage is taken as high level or ‘1’ and the lower positive voltage is taken as low level or ‘0’.

b) Negative Logic System:

In this type of system, the more negative voltage is taken as ‘1’ and the less negative voltage is taken as ‘0’.

c) In Positive logic system +5 V is taken as

‘1’ state and 0 V as ‘0’ state. Terminology of Logic Circuits: Logic Gate:

The logic circuit in which there is one or more than one input but only one output is called a logic gate.

OR gate, AND gate and NOT gate are the basic logic gates. The other gates like the NAND and NOR gates can be obtained from these basic gates.

3. In calculators and computers, the voltage or the current has only two values, the maximum value indicated by ‘1’ and the minimum by ‘0’. Such a signal is known as a digital signal.

4. The number system which has only two symbols (either 0 or 1) is called binary number system. The circuit which handles binary voltage levels is called digital circuit.

5. There are two types of systems adopted for a logic circuit.

a) Positive Logic System: In this type of system, the higher positive voltage is taken as high level or ‘1’ and the lower positive voltage is taken as low level or ‘0’.

b) Negative Logic System: In this type of system, the more negative voltage is taken as ‘1’ and the less negative voltage is taken as ‘0’.

c) In Positive logic system +5 V is taken as ‘1’ state and 0 V as ‘0’ state.

## Terminology of Logic Circuit:

**Logic Gate:**

The logic circuit in which there is one or more than one input but only one output is called a logic gate.

OR gate, AND gate and NOT gate are the basic logic gates. The other gates like the NAND and NOR gates can be obtained from these basic gates.

**Boolean Equation:**

The Boolean equation represents the special type of algebraic representation, which describes the working of the logic gates. Truth Table:

**Truth Table:**

The table which indicates the output for different combinations of the input voltage is known as the truth table.

**OR gate:**

1. The following figure shows the circuit containing the bulb and the two switches S_{1} and S_{2} connected in parallel to illustrate the working of an OR gate.

2. The status of the bulb with respect to the switch positions are shown in table

3. In this table, if the switch A is taken as input A and the switch B is taken as input B and the status of the bulb is taken as output Y, we get the truth table of an OR gate. Boolean equation is given as : Y = A + B is read as “Y is equal to A or B”. Here ‘+’ sign indicates OR operator.

4. Symbol for OR gate

5. Truth table for OR gate

6. Whenever any one or both inputs are ‘1’(high), then we get the output ‘1’ (high).

**AND gate:**

1. The following figure shows the circuit containing the bulb and the two switches A and B connected in series to illustrate the working of an AND gate.

2. The status of the bulb with respect to the switch positions are shown in table

3. In this table, if the switch A is taken as input A and the switch B is taken as input B and the status of the bulb is taken as output Y, we get the truth table of an OR gate. Boolean equation is given as : Y = A.B is read as “Y is equal to A AND B”. Here ‘.’ sign indicates OR operator.

4. Symbol for OR gate

5. Truth table for OR gate

6. Whenever any one or both inputs are ‘0’ (low), then we get the output ‘0’ (low).

**NOT gate:**

1. The NOT gate has only one input and output terminal. This gate inverts the input voltage. When the switch S is open, current flows through the bulb and it is on. When the switch A is closed, no current flows through the bulb and it is off.

2. The status of the bulb with respect to the switch positions are shown in table

3. In this table, if the switch S is taken as input A and the status of the bulb is taken as output Y, we get the truth table of a NOT gate.

The Boolean equation is given as Y = A is read as “Y not equal to A ”. Here ‘-’ sign indicates NOT operator.

6. NOT gate inverts the input voltage. When the input is ‘0’ (low), the output is ‘1’ (high). When the input is ‘1’ (high), the output is ‘0’ (low). Hence this gate is called inverter.

## NOR gate:

1. The NOR gate is constructed by combining the OR gate and the NOT gate ( OR + NOT = NOR ). Here the output of the OR gate is given as input to the NOT gate.

2. The Boolean equation is given as: Y = A + B and is read as “Y is equal to NOT A or B.”

3. The symbol of the NOR gate is as follows

4. The output is ‘0’ whenever any one input is ‘1’. Whenever all the inputs are ‘0’, the output is equal to ‘1’.

5. Truth table for OR gate

## NAND gate:

1. NAND gate is constructed by combining the AND gate and the NOT gate ( AND + NOT = NAND ). Here the output of the AND gate is given as input to the NOT gate.

2. The Boolean equation is given as: Y = A • B and is read as “Y is equal to NOT A and B.”

3. The symbol for NAND gate is

4. The output is equal to ‘1’ when any one input is equal is equal to ‘0’ and the output is equal to ‘0’ when all the inputs are equal to ‘1’.

5. Truth table for OR gate

Note:

Any logic gate of function or complete digital system can be constructed using either NAND gates or NOR gates only. For this reason, they are called universal building block or universal gates.

**Uses of Logic Gates:**

1. Every digital circuit or instrument or system is made up of logic gates.

2. They are used for automatic control of the process in the industry.

3. Arithmetic and logic unit of computers and calculators uses logic gates.

## Integrated Circuits (IC):

1. About 50 years back, the electronic circuits were prepared from transistors, diodes, and resistors by joining them using conducting wires. In the next generation, printed circuit

board ( PCB ) came into existence. Here the electronic components are arranged on a board and connected with the help of metal strips which helped reduce the size of the

electronic circuits.

2. Later, these three-dimensional circuits were made two-dimensional to further reduce their size which gave rise to integrated circuits ( I. C. ) size of which is about 1 mm x 1 mm.

3. In an I. C., a small sized crystal ( or chip ) is taken and transistors, diodes, resistors, and capacitors are internally connected which reduced both the size as well as the cost of

the electronic gadgets.

4. The most widely used technology is the *Monolithic Integrated Circuit. *The word *monolithic *means that the entire circuit is formed on a single silicon crystal (or *chip*).

The connections coming out from the ‘chip’ to the pins that enable it to make external connections.

5. Depending on nature of input signals, IC’s can be grouped in two categories: (a) *linear *or *analogue IC’s *and (b) digital IC’s.

6. The linear IC’s process analogue signals which change smoothly and continuously over a range of values between a maximum and a minimum. The output is more or less directly proportional to the input, i.e., it varies *linearly *with the input. One of the most useful linear IC’s is the operational amplifier.

7. The digital IC’s process signals that have only two values. They contain circuits such as logic gates. Depending upon the level of integration (i.e., the number of circuit components or logic gates), the ICs are termed as Small Scale Integration, SSI (logic gates < 10); Medium Scale Integration, MSI (logic gates < 100);

Large Scale Integration, LSI (logic gates < 1000); and Very Large Scale Integration, VLSI (logic gates > 1000). The technology of fabrication is very expensive but large scale industrial production has made them very inexpensive.