Binary Arithmetic

Binary arithmetic is a very important part of various digital systems. Using various methods, we can perform addition, subtraction, multiplication, and division in binary numbers. These operations are much easier than decimal number arithmetic operations because the binary system has only two digits: 0 and 1. 

Binary arithmetic is essential to all digital computers and many other digital systems .  Binary arithmetic includes the basic arithmetic operations of addition, subtraction, multiplication and division. The following sections highlight the rules that apply to these operations when they are performed on binary numbers. 

Binary Addition

The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0. Most of the functionalities of the computer system use the binary number system. The binary code uses the digits 1’s and 0’s to make certain processes turn off or on. The process of the addition operation is very familiar to the decimal system by adjusting to the base 2. 

Rules of Binary Addition

Binary addition is much easier than the decimal addition when you remember the following tricks or rules. Using these rules, any binary number can be easily added. The four rules of binary addition are:

• 0 + 0 = 0

• 0 + 1 = 1

• 1 + 0 = 1

• 1 + 1 =10

Binary Subtraction

Subtraction of binary numbers is an arithmetic operation similar to the subtraction of decimal numbers or base 10 numbers. For example, 1 + 1 + 1 = 3 in base 10 and 1 + 1 + 1 = 11 in binary number system. When you add and subtract binary numbers, you will need to be careful when borrowing as these will take place more often.

When you subtract several columns of binary digits, you must take into account the borrowing. When 1 is to be subtracted from 0, the result is 1 where 1 is borrowed from the next highest order bit or digit.

Binary Subtraction Rules

Rules and tricks: Binary subtraction is much easier than the decimal subtraction when you remember the following rules:

• 0 – 0 = 0

• 0 – 1 = 1 ( with a borrow of 1)

• 1 – 0 = 1

• 1 – 1 = 0

Binary Multiplication:

Binary multiplication is similar to decimal multiplication. However, as there are only 2 bits, 0 and 1, It is much simpler than decimal multiplication because there are only two possible results of multiplying two bits. There are four rules of binary multiplication.

     Rules of Multiplication:

1.    0*0

           = 0 

2.      0*1

           = 0

 3.     1*0

           = 0

 4.    1*1

          = 1

Binary Division:

Binary division, similar to other binary arithmetic operations, is performed on binary numbers. The algorithm for binary division is somewhat similar to decimal division, the only difference here lies in the rules followed using the digits '0' and '1'. Binary multiplication and binary subtraction are the two binary arithmetic operations that are performed while performing binary division. The use of only '0' and '1' makes binary division quite simpler in comparison to decimal division. Other operations that are used while performing binary division are binary multiplication and binary subtraction.  There are four parts in any division: Dividend, Divisor, quotient, and remainder. 

How To Do Binary Division:

Binary division problems can be solved by using the long division method, which is one of the most efficient and easiest ways to divide binary numbers.