Download Binary Arithmetic Computation and more Papers Information and Computer Technology in PDF only on Docsity!
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 =
How To Do Binary Addition?
Now, look at the example of the binary addition:101 + 101 Procedure for Binary Addition of Numbers: 101 (+) 101
- Step 1: First consider the 1โs column, and add the oneโs column,( 1+1 ) and it gives the result 10 as per the condition of binary addition.
- Step 2: Now, leave the 0 in the oneโs column and carry the value 1 to the 10โs column. 1 101 (+) 101 โโโโโ 0
- Step 3: Now add 10โs place, 1+( 0 + 0 ) = 1. So, nothing carries to the 100โs place and leave the value 1 in the 10โs place 1 101 (+) 101 โโโโ- 10
- Step 4: Now add the 100โs place ( 1 + 1 ) = 10. Leave the value 0 in the 100โs place and carries 1 to the 1000โs place. 1 101 (+) 101 โโโโ- 1010 So, the resultant of the addition operation is 1010. When you cross-check the binary value with the decimal value, the resultant value should be the same. The binary value 101 is equal to the decimal value 5 So, 5 + 5 = 10 The decimal number 10 is equal to the binary number 1010.
Examples of Binary Addition
A few examples of binary additions are as follows: Example 1: 10001 + 11101 Solution: 1 1 0 0 0 1 (+) 1 1 1 0 1 โโโโโโโโ 1 0 1 1 1 0 Example 2: 10111 + 110001 Solution: 1 1 1 1 0 1 1 1 (+) 1 1 0 0 0 1 โโโโโโโโ 1 0 0 1 0 0 0
ii) 111 from 1000
Solution:
111 from 100 0
1 Borrow
Example 1: 0011010 โ 001100 Solution: 1 1 Borrow 0 0 1 1 0 1 0 (-) 0 0 1 1 0 0 โโโโโโ 0 0 0 1 1 1 0 Decimal Equivalent : 0 0 1 1 0 1 0 = 26 0 0 1 1 0 0 = 12 Therefore, 26 โ 12 = 14 The binary resultant 0 0 0 1 1 1 0 is equivalent to the 14
Example 2: 0100010 โ 0001010 Solution: 1 1 Borrow 0 1 0 0 0 1 0 = 34 10 (-) 0 0 0 1 0 1 0 = 10 10 โโโโโโ 0 0 1 1 0 0 0 = 24 10
Binary Multiplication
Binary Multiplication
Binary multiplication is one of the four binary arithmetic. The other three fundamental operations are addition, subtraction and division. In the case of a binary operation, we deal with only two digits, i.e. 0 and 1. The operation performed while finding the binary product is similar to the conventional multiplication method. The four major steps in binary digit multiplication are:
- 0 ร 0 = 0
- 0 ร 1 = 0
- 1 ร 0 = 0
- 1 ร 1 = 1 Note: The binary product of the two binary numbers 1 and 1 is equal to 1 only. And no additional number is borrowed or carried forward in this operation. Based on the above specification, we will solve here the problems online based on the multiplication of binary numbers. In this section, you will get answers for the questions about binary multiplication, including:
- What is Binary multiplication?
- Procedure to multiply two binary numbers
- Steps to Solve Binary multiplication using examples
What is 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, and finally, the addition operation is made. Similar to the decimal system, the multiplication of the binary numbers is done by multiplying the multiplicand with the multiplier. It is noted that the multiplication by zero makes all the bits zero, and this step may be ignored in the intermediate steps. The multiplication by 1 makes all the multiplicand value unchanged.
0+0 = 0 0 - 0 = 0 0รท0 = 0
0 - 1 = 1 (1 is
borrowed)
0รท1 = 0
1+0 = 1 1 - 0 = 1 1รท1 = 1
1+1 = 0 (1 is carry
forwarded)
Examples of Binary Multiplication Some binary multiplication examples are given below for a better understanding of this concept. Example 1 : Solve 1010 ร 101 Solution: 1010 ร 101 1010 (ร) 101 โโโโโโ 1010 0000 โโโโโโ 01010 โฆโฆ. First Intermediate Sum 1010 โโโโโโโ 110010 Comparison with Decimal values: 10102 = 1 (^010) 10102 = (^510) 10 x 5 = 5 (^010) (110010) 2 = 5 (^010) Another example of binary multiplication with a decimal point is as follows: Question: 1011.01 ร 110. Solution:
Binary Division
What is Binary Division?
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. Long division is one
of them and the easiest and the most efficient way. This section has been designed to answer
questions about binary division, including:
- What is Binary division?
- Procedure to add two binary numbers
- Examples to Solve Binary division
Binary Division Rules
The binary division is much easier than the decimal division when you remember the following
division rules. The main rules of the binary division include:
โข 1รท1 = 1
- 1รท0 = Meaningless
- 0รท1 = 0
- 0รท0 = Meaningless
Similar to the decimal number system, the binary division is similar, which follows the four-step
process:
- Step 1: First, look at the first two numbers in the dividend and compare with the divisor. Add the number 1 in the quotient place. Then subtract the value, you get 1 as remainder.
- Step 2: Then bring down the next number from the dividend portion and do the step 1 process again
- Step 3: Repeat the process until the remainder becomes zero by comparing the dividend and the divisor value.
- Step 4: Now, in this case, after you get the remainder value as 0, you have zero left in the dividend portion, so bring that zero to the quotient portion.
Therefore, the resultant value is quotient value which is equal to 111110
So, 01111100 รท 0010 = 111110
Example 2: Solve using the long division method: 101101 รท 101
Solution:
So, when you bring down the fourth bit of the dividend, it does not match with the divisor. In
order to bring down the 5 th^ and 6 th^ bit of the dividend, add two zeros in the quotient value.
