Logic Gates
A gate is a type of digital circuit that has one or more input voltages, but only one output voltage. OR gate, AND gate, and NOT gate are three gates. These gates are basic gates that can be connected in different ways to create various circuits. This circuit can perform arithmetic calculations and make logical decisions like the human brain. In 1854, English mathematician George Boole invented a type of mathematics. This math is known as Boolean algebra. Boolean algebra does the mathematical analysis of logic. Gates can perform various Boolean algebraic operations and thus make logical decisions. For this reason, gates are known as logic gates or logic circuits.
Boolean algebra
Let’s say you do something. Is that work right or wrong? Is a statement given by you true or false? A little thought reveals that most of what we usually think about is trying to find answers to these ‘two-valued answers’ questions. The Greek philosopher Aristotle first discovered the method of discovering truth by finding the answers to several ‘two-valued answers’ questions about the same topic. After this, many mathematicians understand that it is possible to express our ideas or logic step by step through some algebraic process. Notable among them is the British mathematician Augustus De Morgan, who almost discovered the link between logic and mathematics. After this George Boole did the rest. The technology that could be improved with Boolean algebra, however, was not immediately understood. Almost 100 years later in 1938, the American applied mathematician Claude Elwood Shannon first used this algebra in a telephone switching circuit. It was only then that technologists realized that Boolean algebra was of immense importance for analyzing and designing computer circuits.
OR Gate
An OR gate has two or more input voltages or signals and an output voltage or signal like any other gate. This gate is called an OR gate because, when either input voltage is high, the output voltage is also high. For example, an OR gate with two inputs will have a high output voltage only if at least one input voltage is high.
Working principle of OR gate
How the OR gate works is very easy to understand in the figure. In a circuit, two switches A and B are connected in parallel. obviously,
- The bulb does not turn on when both switches are in the off position; In this case, the output is zero, i.e., no output is available.
- When either switch A and switch B are off and the other is on, the bulb turns on, i.e., the output is available.
- Even when both switches are in the ON position, the bulb turns on, i.e., output is available.
So, this circuit works like an OR gate. However, it should be remembered that the use of this type of circuit as a logic gate is almost non-existent.
OR gate in electronic circuit
The figure shows an electronic OR gate with two inputs. A simple form of this circuit is also shown. The input voltages are denoted by A and B and the output voltage is denoted by Y. Suppose, the two possible states of the input voltage are low (say, 0 V) and high (say, 5 V).
The resistor RL is permanently connected to the circuit. The gate can be in any one of the following four states.
- A is low and B is low: In this case the output voltage is low. According to the diagram, if A and B are low, the diodes are in two non-conducting states. As a result, Y is also lower.
- A is low and B is high: In this case the output voltage is high. As per the figure, if A is low then the diode connected to A is non-conducting. But if B is high, the diode connected to B is forward-biased. As a result, Y remains high.
- A is high and B is low: In this case the output voltage is high. As per the figure, if B is low then the diode connected to B is non-conducting. But if A is high, the diode connected to A is forward-biased, so Y is high.
- A is high and B is high: In this case the output voltage is high. As per the figure, if A and B are high then the diodes connected to them are forward-biased. As a result, Y remains high.
Truth table
A list of possible inputs and outputs of a gate can be made. This list is called the truth table of that gate. Below is the truth table of a ‘two-input OR gate’.
| A | B | Y |
|---|---|---|
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
Since any single input or single output of a gate can have only two states—low or high—it is convenient to express this state in binary numbers. The above truth table is constructed by representing the low state as 0 and the high state as 1. A quick look at the table shows that if one of the two inputs has a state of 1, then the output has a state of 1. That is, the state of Y is 1 if the state of either A or B is 1 and if the state of A and B is 1. In other words, the OR gate is an ‘any-or-all’ gate; The state of the output is 1 if the state of ‘any or all’ inputs is 1.
Positive and negative logic: The method of assuming a low state as 0 and a high state as 1 is called positive logic. On the other hand, there is no problem assuming the low state is 1 and the high state is 0—this is called negative logic. In this case, it should be noted that the same logic must be used—either positive or negative. Do not mix the two logics at the same time.
Truth table
The OR gate symbol is shown in the figure. Digital circuits are drawn using this symbol.
Boolean algebra related to OR gate
In Boolean algebra, the ‘+’ sign denotes the ‘OR’ process. The Boolean algebraic equation for the OR gate shown in the figure is,
This equation is read as— “Y equals to A or B”.
When A = 0 = B, then Y = 0 + 0 = 0
When A = 0 and B = 1, then Y = 0 + 1 = 1
When A = 1 and B = 0, then Y = 1 + 0 = 1
When A = 1 = B, then Y = 1 + 1 = 1
Of these, the 1 + 1 = 1 relationship in the last line is noteworthy.
Figure shows the circuit of an OR gate with three inputs, symbols, Boolean algebraic equation and truth table.
| Input | Output | ||
|---|---|---|---|
| A | B | C | Y |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Special note
- OR, AND, and NOT gates are called basic logic gates. Because any other logic gate is some combination of these three basic gates.
- Not all logic gates can be constructed using any of the three basic gates. For example, an AND gate or a NOT gate cannot be obtained by combining multiple OR gates. However, NOR and NAND gates can be made by combining OR, AND, and NOT gates. The peculiarity of this dual gate is that, given a large number of NOR data, all kinds of logic gates can be made by specially combining them—as is the case with NAND gates. This is why NOR and NAND gates are called universal logic gates, although neither of them are fundamental gates.
- De Morgan’s theorem is used to construct various logic gates using multiple basic gates.
De Morgan’s theorem
- (A ∪ B)’ = A’ ∩ B’
- (A ∩ B)’ = A’ ∪ B’
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