Logic Gates by electronicblog.in

A logic gate is an idealized or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device.

Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.

Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and computer memory, all the way up through complete microprocessors, which may contain more than 100 million gates. In modern practice, most gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors).

There are 8 different logic gates, they are:

- Buffer gate
- NOT gate
- AND gate
- OR gate
- NAND gate
- NOR gate
- X-OR gate
- X-NOR gate

One by one we will see each gate in detail:

1. **Buffer gate**

A buffer, is a basic logic gate that passes its input, unchanged, to its output. Its behavior is the opposite of a NOT gate. The main purpose of a buffer is to regenerate the input, usually using a strong high and a strong low. A buffer has one input and one output; its output always equals its input. Buffers are also used to increase the propagation delay of circuits by driving the large capacitive loads.

Boolean expression between input and output is: OUTPUT = INPUT

2. **NOT gate**

The NOT gate is a single input single output gate. This gate is also known as Inverter because it performs the inversion of the applied binary signal, i.e., it converts 0 into 1 or I into 0. In other words, the gate which has high input signal only when their input signal is low such type of gate is known as the not gate.

Boolean expression between input and output is: OUT = -A

3. **AND gate**

The AND gate is a basic digital logic gate that implements logical conjunction – it behaves according to the truth table to the right. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If none or not all inputs to the AND gate are HIGH, a LOW output results. The function can be extended to any number of inputs.

Boolean expression between input and output is: OUTPUT = A^B or A&B

4. **OR gate**

The OR gate is a digital logic gate that implements logical dis-junction . A HIGH output (1) results if one or both the inputs to the gate are HIGH (1). If neither input is high, a LOW output (0) results. In another sense, the function of OR effectively finds the *maximum* between two binary digits, just as the complementary AND function finds the minimum*.*

Boolean expression between input and output is: OUTPUT = A+B

5.** NAND gate **

a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan’s theorem, a two-input NAND gate’s logic may be expressed as AB=A+B, making a NAND gate equivalent to inverters followed by an OR gate.

The NAND gate is significant because any boolean function can be implemented by using a combination of NAND gates. This property is called functional completeness. It shares this property with the NOR gate. Digital systems employing certain logic circuits take advantage of NAND’s functional completeness.

Boolean expression between input and output is: OUTPUT = -(A&B)

6. **NOR gate**

The NOR gate is a digital logic gate that implements logical NOR – it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator. It can also in some senses be seen as the inverse of an AND gate. NOR is a functionally complete operation—NOR gates can be combined to generate any other logical function. It shares this property with the NAND gate. By contrast, the OR operator is *monotonic* as it can only change LOW to HIGH but not vice versa.

Boolean expression between input and output is: OUTPUT = -(A+B)

7. **X-OR gate**

XOR gate is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is “must have one or the other but not both”.

Boolean expression between input and output is: OUTPUT = (A & -B) + (B & -A)

8. **X-NOR gate**

he XNOR gate is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an “equivalence gate”. A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.

Boolean expression between input and output is: OUTPUT = (A & B) + (-A & -B)