Digital Electronics and Logic Gates

Digital Electronics And Logic Gates

Electronics can be broadly divided into two categories: analog electronics and digital electronics. Analog electronics deals with signals that vary continuously over a range of values, such as voltage from a microphone or current in a circuit with continuously changing resistance. Digital electronics, on the other hand, deals with signals that have discrete values, typically represented by two levels: HIGH and LOW, often corresponding to different voltage levels. These two levels represent binary digits (bits), usually 1 and 0.

Digital electronics forms the basis of modern computing and digital systems. Information (like numbers, text, images, audio, video) is processed and stored in binary form. Digital circuits perform logical operations on these binary inputs to produce binary outputs. These operations are carried out by fundamental building blocks called logic gates.

Logic Gates (AND, OR, NOT, NAND, NOR)

A logic gate is an elementary electronic circuit that performs a logical operation on one or more binary inputs and produces a single binary output. Logic gates are the basic components of digital circuits. They are typically implemented using semiconductor devices like diodes and transistors, often integrated into complex integrated circuits (ICs).

The operation of a logic gate can be described by a Boolean expression and represented visually by a logic symbol and a truth table. A truth table lists all possible combinations of binary inputs and the corresponding output.

Basic Logic Gates

There are three fundamental logic gates: AND, OR, and NOT. All other logic operations and gates can be constructed by combining these basic gates.

AND Gate:
- Operation: The output is HIGH (1) only if all the inputs are HIGH (1). Otherwise, the output is LOW (0). It performs logical multiplication.
- Boolean Expression: If inputs are A and B, output Y. $Y = A \cdot B$ or $Y = AB$
- Logic Symbol:
- Truth Table (for 2 inputs):
  
  A B Y = A $\cdot$ B
  
  0 0 0
  
  0 1 0
  
  1 0 0
  
  1 1 1
OR Gate:
- Operation: The output is HIGH (1) if at least one of the inputs is HIGH (1). The output is LOW (0) only if all the inputs are LOW (0). It performs logical addition.
- Boolean Expression: If inputs are A and B, output Y. $Y = A + B$
- Logic Symbol:
- Truth Table (for 2 inputs):
  
  A B Y = A + B
  
  0 0 0
  
  0 1 1
  
  1 0 1
  
  1 1 1
NOT Gate (Inverter):
- Operation: The output is the inverse or complement of the input. If the input is HIGH (1), the output is LOW (0). If the input is LOW (0), the output is HIGH (1). It has only one input.
- Boolean Expression: If input is A, output Y. $Y = \bar{A}$ or $Y = A'$ (read as "A NOT" or "A bar")
- Logic Symbol:
- Truth Table (for 1 input):
  
  A Y = $\bar{A}$
  
  0 1
  
  1 0

A	B	Y = A $\cdot$ B
0	0	0
0	1	0
1	0	0
1	1	1

A	B	Y = A + B
0	0	0
0	1	1
1	0	1
1	1	1

A	Y = $\bar{A}$
0	1
1	0

Universal Logic Gates

NAND and NOR gates are called universal gates because any other logic gate (AND, OR, NOT, XOR, XNOR) can be implemented using only NAND gates or only NOR gates.

NAND Gate (NOT-AND):
- Operation: The output is HIGH (1) only if at least one of the inputs is LOW (0). It is the complement of the AND gate's output. Output is LOW (0) only if all inputs are HIGH (1).
- Boolean Expression: If inputs are A and B, output Y. $Y = \overline{A \cdot B}$ or $Y = (A \cdot B)'$
- Logic Symbol:
  
  (AND symbol followed by a small circle/bubble at the output, indicating inversion)
- Truth Table (for 2 inputs):
  
  A B Y = $\overline{A \cdot B}$
  
  0 0 1
  
  0 1 1
  
  1 0 1
  
  1 1 0
NOR Gate (NOT-OR):
- Operation: The output is HIGH (1) only if all inputs are LOW (0). It is the complement of the OR gate's output. Output is LOW (0) if at least one input is HIGH (1).
- Boolean Expression: If inputs are A and B, output Y. $Y = \overline{A + B}$ or $Y = (A + B)'$
- Logic Symbol:
  
  (OR symbol followed by a small circle/bubble at the output, indicating inversion)
- Truth Table (for 2 inputs):
  
  A B Y = $\overline{A + B}$
  
  0 0 1
  
  0 1 0
  
  1 0 0
  
  1 1 0

A	B	Y = $\overline{A \cdot B}$
0	0	1
0	1	1
1	0	1
1	1	0

A	B	Y = $\overline{A + B}$
0	0	1
0	1	0
1	0	0
1	1	0

Other Common Logic Gates (Derived)

Other gates like XOR (Exclusive-OR) and XNOR (Exclusive-NOR) are also commonly used but can be constructed from the basic gates.

XOR Gate: Output is HIGH if an odd number of inputs are HIGH. For two inputs A, B, $Y = A \oplus B = A\bar{B} + \bar{A}B$.
XNOR Gate: Output is HIGH if an even number of inputs are HIGH (including zero inputs HIGH). For two inputs A, B, $Y = A \odot B = A B + \bar{A}\bar{B}$. It is the complement of XOR.

Logic gates are the fundamental building blocks used to design combinational logic circuits (whose output depends only on the current inputs) and sequential logic circuits (whose output depends on current inputs and past inputs, involving memory elements like flip-flops). These circuits are used in everything from simple switches to complex microprocessors.

Example 1. Determine the output of a 2-input AND gate if the inputs are A=1 and B=0.

Answer:

Given input values for a 2-input AND gate: A=1 and B=0.

The AND gate produces an output of HIGH (1) only if both inputs are HIGH (1). Otherwise, the output is LOW (0).

In this case, one input (A=1) is HIGH, but the other input (B=0) is LOW. Since both inputs are not simultaneously HIGH, the output will be LOW.

Using the truth table for an AND gate, for input combination (1, 0), the output is 0.

Therefore, the output of the AND gate is 0.

Example 2. What is the output of a NOT gate if the input is 1?

Answer:

Given input value for a NOT gate: Input = 1.

A NOT gate (inverter) produces an output that is the inverse (complement) of its input. If the input is 1 (HIGH), the output is 0 (LOW). If the input is 0 (LOW), the output is 1 (HIGH).

In this case, the input is 1.

Therefore, the output of the NOT gate is 0.