The number system in digital electronics is the fundamental concept whose knowledge is a prerequisite for learning the other concepts. As we know, digital electronics is a field of engineering that involves analyzing and implementing numbers and logic based on numbers.
In this article, we will cover all the essential concepts of number systems required to study digital electronics.
What is a Number System in Digital Electronics?
A number system is a technical method of representing different numbers and defining protocols to perform operations on these numbers.
A number system provides a systematic way of expressing numbers and assigning their values. A number system uses a set of symbols to represent the value of a numeral. It also provides some definite rules to perform various operations like addition, multiplication, division, etc.
In our daily life, we use the decimal number system, which is basically a base-10 number system that provides 10 symbols to represent different numeric values uniquely.
Although, there are several other types of commonly used number systems like binary, octal, and hexadecimal number systems.
Types of Number System in Digital Electronics
Based on the base or radix of the number system, there can be various types of number systems. But, the following four number systems are most commonly used in digital electronics.
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
Let us discuss each type of number system in detail.
1). Decimal Number System
The decimal number system is the most widely used type of number system by humans. It is also known as the base-10 number system, as it utilizes 10 unique symbols to represent each numeral. These ten unique symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
One important thing to note about the decimal number system is that it is a weight number system, which means the value of a digit in a number depends on its position within the number. The positional value of a digit in a number is simply determined by multiplying the digit by a corresponding power of 10.
To understand it in more detail, consider the following decimal number and its evaluation.
Decimal number = 5234
5234
=(5 × 103) + (2 × 102) + (3 × 101) + (4 × 100)
= 5000 + 200 + 30 + 4 = 5234
The decimal number system is widely used by us in everyday life to perform various basic calculations. It is also used in different professional calculations in various fields such as finance, management, technology, science, etc. It is the most human-friendly number system.
(2). Binary Number System
A binary number system is another commonly used number system. It is a base-2 number system, as it has only two unique symbols namely, 0 and 1, to specify numerical values. The binary number system is mostly used in digital electronic systems to perform switching operations, where the digit 0 represents the `OFF` state of the circuit. In contrast, the digit `1` represents the `ON` state of the circuit.
Each digit in a binary number system is called a `Bit`, i.e. Binary Digit. Similar to the decimal number system, it is also a positional number system in which the value of a digit in a given number is determined by multiplying the digit by its corresponding power of the base, i.e. 2.
For example, consider a binary number 1001101.
The decimal value of this binary number is obtained as follows:
1001101
=(1 × 26) + (0 × 25) + (0 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20)
=64 + 0 + 0 + 8 + 4 + 0 + 1 = 77
Therefore, the value of the binary number 1001101 in decimal is equal to 77.
The binary number system is considered the backbone of digital electronics and information technology. As it can efficiently represent the switching state of a device, i.e. on or off.
Also, it can be used to perform various arithmetic and logical operations required in digital processing like storage, communication, etc.
(3). Octal Number System
The octal number system is another essential number system used in some digital electronic applications. It is basically a base-8 number system, having 8 unique symbols 0, 1, 2, 3, 4, 5, 6, and 7 to represent numerical values.
It is also a positional weighted number system in which the weight or value of a digit in a number is obtained by multiplying the digit by its corresponding power of base, i.e. 8.
For example, consider the octal number 5427. The value of this number in the decimal system is obtained as follows:
5427
=(5 × 83) + (4 × 82) + (2 × 81) + (7 × 80)
= (5 × 512) + (4 × 64) + (2 × 8) + (7 × 1)
=2560 + 256 + 16 + 7 = 2839
Hence, the value of the octal number 5427 in the decimal number system is equal to 2839.
The octal number system is also used in various applications of digital electronics like storage, error detection, debugging, memory addressing, and more.
(4). Hexadecimal Number System
The hexadecimal number system is a base 16 number system having 16 unique symbols to represent the numerical values. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (10), B (11), C (12), D (13), E (14), and F (15). Similar to the other three number systems, it is also a positional weighted number system, where the value of the digit depends on its position within the number.
For example, consider a hexadecimal number 13AE. The decimal value of this hex number is obtained as follows:
13AE
=(1 × 163) + (3 × 162) + (10 × 161) + (14 × 160)
= 4096 + 768 + 160 +14 = 5038
Therefore, the value of the hexadecimal number 13AE in the decimal number system is equal to 5038.
The hexadecimal number system has several applications in digital electronics, such as memory addressing, programming, color representations, debugging, etc.
Conversion Table of Number Systems in Digital Electronics
The following is the conversion table using which we can easily convert a number given in one number system into another one.
| Decimal Number System (Base 10) | Binary Number System (Base 2) | Octal Number System (Base 8) | Hexadecimal Number System (Base 16) |
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
Conclusion of Number System
In conclusion, this is all about the number system and its different types. The number system is a systematic way of expressing numbers and their associated rules. The most widely used types of number systems in digital electronics are decimal, binary, octal, and hexadecimal number systems. Each of these number systems has its own advantages and applications.
