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# Binary Number System

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A number system is of four types: binary number system, decimal number system, hexadecimal number system and octal number system. The binary number system is also known as the base-2 number system. Binary number system represents two numbers 0 and 1. Binary number system performs mathematical operations like addition, subtraction, division and multiplication.

Binary addition is similar to the normal addition process. We just add together the ones, tens, hundreds and so on of all the numbers to be added. The points to be remembered in Binary Addition are:

0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0; carry 1

Binary subtraction is also easy. We just need to subtract the ones, tens and hundreds of the numbers. If there was a need to borrow then the borrowed number becomes 10 whereas the number from which it is borrowed becomes 0. The four points to be remembered in Binary Subtraction are:
0 - 0 = 0
1 - 0 = 1
0 - 1 = 1; borrow 1,
1 - 1 = 0

Binary multiplication is the same as normal multiplication. Binary addition is also required during the multiplication process. The following rules are to be remembered while performing Binary Multiplication:
0 * 0 = 0
1 * 0 = 0
0 * 1 = 0
1 * 1 = 1

Binary division is not easy as other mathematical operation when solving with complex numbers. It requires binary subtraction. The four rules for Binary Division are:
0 ÷ 0 = 0; Remainder = 0
1 ÷ 0 = 0; Remainder = 1
0 ÷ 1 = 0; Remainder = 0
1 ÷ 1 = 1; Remainder = 0

The other operations that are performed on this binary numbering system are one’s complement and two’s complement. Also the binary number system can be converted into any other number system such as the decimal number system, hexadecimal number system and octal number system. The different logic gates made using binary number system are AND gate, OR gate, NOT gate, XOR gate, NOR gate. All this gates are used in implementing different circuit system.