BINARY ARITHMETIC

 BINARY ARITHMETIC

                       Binary arithmetic is used in digital systems mainly because the numbers (decimal and floating-point numbers) are stored in binary format in most computer systems. All arithmetic operations such as addition, subtraction, multiplication, and division are done in binary representation of numbers.

 

 

 

1) BINARY ADDITION;

Binary Addition It is a key for binary subtraction, multiplication, division. There are four rules of binary addition. In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given column and a carry of 1 over to the next column.

   Basic arithmetic operations like addition, subtraction, multiplication, and division, play an important role in mathematics.

 

  

 

2) BINARY SUBTRACTION;

 In binary subtraction, the only case where borrowing is necessary is when 1 is subtracted from 0. When this occurs, the 0 in the borrowing column essentially becomes "2" (changing the 0-1 into 2-1 = 1) while reducing the 1 in the column being borrowed from by 1.

   When a large digit is to be subtracted from a smaller one, a 'borrow' is taken from the next column to the left. In decimal subtractions the digit 'borrowed in' is worth ten, but in binary subtractions the 'borrowed in' digit must be worth 210 or binary 102.

RULES

 To subtract a larger number from a smaller one, switch the order of the numbers, do the subtraction, then add a negative sign to the answer. For example, to solve the binary problem 11 - 100, solve for 100 - 11 instead, then add a negative sign to the answer.

 

3) BINARY MULTIPLICATION;

The binary multiplication operation is actually a process of addition and shifting operation. This process has to be continued until all the multiplier is done.

 

        Multiplication in binary is exactly as it is in decimal, i.e. multiply numbers right to left and multiply each digit of one number to every digit of the other number, them sum them up. The 3 basic binary multiplication rules are also similar to decimal.

 

 What is the value of n in multiplication of 110* 1000? 

   Explanation: In Booth's, n denotes the number of bits that the higher binary number has when multiplication is performed. Here, since there are 4 bits in 1000, the answer is n=4. 9.

 

 

 

 

 

 

4)BINARY DEVISION;

Binary Division:

 

  Step 1: First, look at the first two numbers in the dividend and compare with the divisor.

 Step 2: Add the number 1 in the quotient place. Then subtract the value, you get 1 as remainder. 

 Step 3: Repeat the process until the remainder becomes zero by comparing the dividend and the divisor value

 

 

       The binary division operation is similar to the base 10 decimal system, except the base 2. The division is probably one of the most challenging operations of the basic arithmetic operations. There are different ways to solve division problems using binary operations.

 

 

 

RULES FOR BINARY ARITHMETIC OPERATIONS

 

 

                     MORE DETAILS;

            https://youtu.be/0WRU6aiGP5w

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