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# Positive and Negative Logic in Digital Electronics

In digital electronics, a **logic** or **logic function** is one that follows the rules that governs a
logical statement. Logics are implemented by using switching networks, where a switching
network is one that is designed by interconnecting a finite number of switches.

**Example** − Let "𝒚" is a logic function, then it may be expressed as,

$$\mathrm{Y = f\left ( x_{i} \right ) }$$

Where, **x _{i}** represents the inputs to the logic network or switching network, and

**y**is the output of the network.

There is another term associated with the logic function that is the **truth table**. The truth
table is used for testing the performance of the logic network. Another important point about
logic systems is that they accept only two values namely 0 and 1. Here, 0 (binary zero)
represents turn-off state of the circuit, while 1 (binary one) denotes the turn-on state of the
logic circuit. Thus, in the truth table of a logic network, the entries are made using 0s and 1s.

The common examples of logic functions are OR, AND, NOT, NAND, NOR, XOR, XNOR, etc. Using these functions, we can implement more complex logic functions as well.

The logic in digital electronics are classified into two types −

- Positive Logic
- Negative Logic

Now, let us discuss, the positive and negative logic in detail.

As discussed above, in digital systems, the variables associated with operations can have only two values, i.e. 0 and 1. Where, 0 and 1 represents the OFF (Logic LOW) and ON (Logic HIGH) state of the system respectively.

## What is Positive Logic?

In digital electronic systems, if the high value of signal (voltage or current) is used to
represent the logic 1 and the low value of signal (voltage or current) is used to represent the
logic 0, then it is called a **positive logic system**.

The pulse waveform representation of a positive logic is shown in Figure-1. In the case of positive logic, the voltage at 0 volts level represents the logic 0 (Logic LOW), and the voltage at +VCC volts level represents the logic 1 (Logic HIGH).

In the generalized form, the positive logic is expressed as,

$$\mathrm{Higher\: Voltage = Logic\: HIGH}$$

$$\mathrm{Lower \: Voltage = Logic\: LOW}$$

**Example of Positive Logic** − Consider an NPN transistor. If the transistor is OFF, then its
output will be at +VCC that represents the logic 1 (HIGH) state. On the other hand, if the
transistor is ON, then its output will be 0 volts, and it represents the logic 0 (LOW) state.

## What is Negative Logic?

In digital electronic systems, if the high value of signal (voltage or current) is used to
represent the logic 0 and the low value of signal (voltage or current) is used to represent the
logic 1, then it is called a **negative logic system**.

The pulse waveform representation of a negative logic is shown in Figure-2. In the case of negative logic, the voltage at -VCC volts level represents the logic 0 (Logic LOW), and the voltage at 0 volts level represents the logic 1 (Logic HIGH).

In the generalized form, the negative logic is expressed as,

$$\mathrm{Higher\: Voltage = Logic\: LOW (0)}$$

$$\mathrm{Lower \: Voltage = Logic\: HIGH (1)}$$

**Example of Negative Logic** − Consider a PNP transistor. If the transistor is OFF, then its
output will be at -VCC volts that represents the logic 0 (LOW) state. On the other hand, if the
transistor is ON, then its output will be 0 volts, and it represents the logic 1 (HIGH) state.

**Note** − It is interesting to know that an OR gate in positive logic is equivalent to an AND gate
in negative logic and **vice-versa**. Similarly, a NOR gate in positive logic is equivalent to a
NAND gate in the negative logic and **vice-versa**.

## Conclusion

All digital systems use the binary number system. Hence, all the digital electronic systems have two states namely, HIGH and LOW, where HIGH is represented by Binary 1 and LOW is represented by Binary 0.

Based on the system response, the digital logics are classified into two types namely **positive
logic** and **negative logic**. In the positive logic, the high voltage level is used to represent logic
1 and the low voltage level is used to represent the logic 0. On the other hand, in the negative
logic, the high voltage level represents the logic 0 and the low voltage level represents the
logic 1.

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