Electronic Essentials: Analogue and Digital Signals, Binary Operations and Logic Gates Revision Notes

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17.1Electronic Essentials: Analogue and Digital Signals, Binary Operations and Logic Gates


In these revision notes for Electronic Essentials: Analogue and Digital Signals, Binary Operations and Logic Gates, we cover the following key points:

  • What are electronic circuits?
  • What are signals? What is the difference between the two types of signals?
  • What is the binary system? Why it is used in digital electronics?
  • How do we do the four basic operations in binary system?
  • What is Boolean Algebra? How is it applied in electronics?
  • What are logic gates?
  • What are the outputs of each logic gate when the inputs are known?

Electronic Essentials: Analogue and Digital Signals, Binary Operations and Logic Gates Revision Notes

An electronic circuit is any circuit containing electronic components such as microchips, capacitors, resistors, diodes, transistors, inductors, coils, transformers etc.

An electronic system works on the base of signals, which are tiny changes in current that occur when the external source oscillates. The device used to convert sound waves to EM waves and vice-versa is known as "processor". It is the "brain" of all electronic systems.

Roughly speaking, an electronic system is composed by three main parts: input (sensor), processing unit (processor) and output.

Sinusoidal signals such as sound waves or EM waves may take any value between zero and their amplitude; they are called analogue signals.

On the other hand, there are electronic systems, which operate by combining only two types of signals: HIGH and LOW (ON and OFF). These are known as digital signals. In other words, in digital systems there is a fixed number of known inputs and outputs which are combined together to give a certain result. Digital signals are produced when there are only two possible input voltages: 0V (LOW) and 5V (HIGH). Symbolically, the LOW voltage is denoted as 0 and the HIGH voltage is denoted by 1. This is just for convenience, i.e. to make these values appear easier on the screen. If we consider only one of these signals (one 0 or 1), this represents a bit (binary digit).

Any combination of 8 bits gives one Byte. In other words, 1 Byte represents the binary number obtained by the combination of 8 different input signals (either 0V or 5V input voltages).

In daily life, we use the decimal system to represent numbers. This is a base 10 number system, i.e. there are 10 digits used to represent the numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In digital electronics however, we use the binary system instead of decimal system. This system contains only two digits: 0 and 1 and its place values are powers of 2 instead of powers of 10.

Another number system widely used in digital electronics is the hexadecimal system. It is a number of system containing 16 digits, from 0 to 15. However, the numbers from 10 to 15 are expressed using the letters from A to F instead of digits.

We can do the four basic operations (addition, subtraction, multiplication and division) in the binary system in the same way as we do them in the decimal system. We can also express the decimal numbers written in base 10 number system using the decimal place to divide the whole and the non-whole part of the number.

The English mathematician George Boole introduced several relationships between the mathematical quantities that contain only two values: either True or False, which can also be denoted by a 1 or 0 respectively. This system was later given the name "Boolean Algebra". The results of all mathematical operations performed on these values can also possess only two values: 1 or 0.

Logic gates are small electronic devices. They contain two inputs and a single output, which perform a Boolean function. Obviously, all data in logic gates are binary digits.

The seven basic operations of Boolean Algebra are: AND, OR, NOT, NAND, NOR, XOR and XNOR. All of them have their own special relationship between inputs and output.

AND operation

This operation gives TRUE (otherwise known as HIGH or 1) as an output when all inputs are TRUE (otherwise known as HIGH or 1). This operation is similar to intersection of sets in the set theory in mathematics. The AND logic operation is represented mathematically by the symbol ( ˄ ) or ( · ) .

OR operation

This operation gives TRUE (otherwise known as HIGH or 1) as an output when at least one of inputs is TRUE (otherwise known as HIGH or 1). This operation is similar to union of sets in the set theory in mathematics. The OR operation is represented mathematically by the symbol ( ˅ ) or ( × ).

NOT operation

This is a logic operation that inverts the value of input. This means when the input is 1 the output is 0 and when the input is 0 the output is 1. The NOT logic operation is shown symbolically through a horizontal line above the input letter (the negation symbol). The NOT operation is the only that does not require necessarily the presence of two inputs. One input is enough to reverse the result of the corresponding output.

NAND operation

NAND is an abbreviation for NOT AND. Thus, a NAND logic operation reverses the output of the corresponding AND. It is represented mathematically through the symbol A ∧ B or simply A · B.

NOR operation

NOR is an abbreviation for NOT OR. Thus, a NOR logic operation reverses the output of the corresponding OR. It is represented mathematically through the symbol A ∧ B or simply A + B̅.

XOR operation

XOR is an abbreviation for EXCLUSIVE OR. It gives HIGH (or 1) when both inputs are the same (both 0 or both 1) and it gives LOW (or 0) when the two inputs are different. The mathematical symbol of XOR logic operation is ⨁.

XNOR operation

XNOR is an abbreviation for EXCLUSIVE NOR (EXCLUSIVE NOT OR). In this logic operation, there is an inversion on the NOR gate to get the XNOR gate. The output is just opposite to that of the XOR gate. If any of the inputs is high (1) excluding the condition of both, the output is low or 0. The mathematical symbol that expresses the XNOR logic operation is ⨀.

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