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The binary number system is commonly used in subjects like mathematics, computers, and many other subjects. The language of a binary number system is understood by only computers. A binary number system is a set of a system of binary numbers. The binary numbers are the numbers that consist of 0 and 1. Binary number is represented with a base of 2. Here we will learn about the binary number system, why we use the binary number system, and how to convert the binary number system to different other systems like decimal systems, etc.
Binary Number System
The binary number system is the number system having base 2. It is the method of representing the numbers in the form of 0 and 1. Here the word itself contains the word ’bi’ which means two numerals which are 0 and 1. You can even change the decimal numbers into binary numbers. The numbers 1 to 10 can be expressed in binary numbers which are mentioned in the below given table.
Decimal Number | Binary Number |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
Binary Number System Logic
The computer performs multiple types of functions by executing the program instructions as per the program logic. As the CPU is the very important component inside a computer system which performs all arithmetic functions and logical operations. The CPU is made of circuits called transistors. The transistors are made of silicon. The transistors in the CPU act as switches.
The logic gates are made of transistors inside a processor chip mainly used by CPU to perform the operations. The computers are digital machines. The logic gates are the basic components in electronics.
A logic gate is the small circuit used in processors for making logical decisions which is used in Boolean Algebra. It is also called binary algebra or logical algebra. We all know it uses binary numbers 0 (zero) and 1 (one).
There are different types of logic gates used in electronics-
- AND gate
- OR gate
- NOT gate
- NAND gate
- NOR gate
The processor is performing the function by reacting to the input of 0s and 1s. After that it gives the result or output based on the input.
Binary Number System Conversion
We can convert binary numbers to decimal systems by converting each digit as a product of the given number which is 0 and 1. They are expressed in 0 and 1 with the respective power of 2.
Operations on Binary Numbers
Binary Addition
The binary addition is done by adding on the binary digits and obtaining the resultant addition.
Binary Number 1 | Binary Number 2 | Addition | Carry |
0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 |
Binary Subtraction
The table below tells about the subtraction of binary digits with the obtained results.
Binary Number 1 | Binary Number 2 | Subtraction | Borrow |
0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 |
0 | 1 | 1 | 1 |
1 | 1 | 0 | 0 |
Binary Multiplication
The below table gives the resultant multiplied result –
Binary Number 1 | Binary Number 2 | Multiplication |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Steps To Convert Decimal to Binary
- In the very first step of the second process, you have to divide the decimal number by 2.
- Now, write the remainder obtained after division.
- Repeat the above two steps, till you get the zero quotients.
- Reverse the remainder and write it.
- Here, you get the required binary number which is equivalent to the given octal number.
Conclusion
In this article we have talked about the binary number system. Binary numbers are the numbers which have only two numbers that are 0 and 1. As the name suggests its binary hence, its two numbers only. We have talked about the binary logic gates. How the binary logic gates are relevant in computers and electronics has also been talked about in detail in this article. There are different types of logic gates which perform different functions and are used to carry out the operations. We have discussed the binary number operations. Binary number addition, subtraction and multiplication tables have been given to understand how to carry out the mathematical operations in binary number systems.
