Addition of two numbers:
Find the addition of 10 an 8?
Let A=10------------> 1 0 1 0
Let B=8--------------> + 1 0 0 0
1 0 0 1 0
Decimal Equivalent of 18 is 10010 which is equivalent to 10+8=18
problem no 1: Find the subtraction value of 10 and 9?
When subtracting a number from another number ( or if a number is negative) then we use one's complement and two's complement notations for a negative number and add the negative number in 1's and 2's complement numbers to the first number.
One's Complement: The one's complement of a number can be obtained by changing the binary digits 0 and 1 of a number to 1 and 0 respectively.
Two's Complement: First find the one's complement of a given number and then add binary number 1 to one's complement
Subtracting two numbers using one's complement number
Let A= 10--------------------> 1010
Let B= -9--------------------->
Binary value of 9 is 1 0 0 1
1's complement of 8 is 0 1 1 0
Now A = 1 0 1 0 ( total four digits)
B = + 0 1 1 0 (total four digits)
Result 1 0 0 0 0 (total five digits )
In this case the left most value( extra bit) is added to the result
Result 0 0 0 0
+ 1
0 0 0 1
The binary equivalent of 0 0 0 1 is decimal value +1 ( 9 - 8 =1)
Problem number 2: Find the value of 8 - 10 using one's complement?
The binary value of 8 is 1000
For -10 value first we fine one' s complement value i.e., -10=0101
Let A= 8 --------------> 1 0 0 0
b= -10
Binary value of 10 is 1 0 1 0
One's complement of 10 is 0 1 0 1
Now we add two's complement of 10 to binary value of 8
A-----------------> 1 0 0 0
B------------------> + 0 1 0 1
1 1 0 1
One at the left most bit indicates negative and the result is in one's complement form
The one's complement of 101 is 010 i.e., 2 and the final value is -2 ( 8 -10 =-2)
Problem no 3: Find the value of 10 - 9 using 2's complement
Two's Complement: First find the one's complement of a given number and then add binary number 1 to one's complement
Binary value of 10 is 1 0 1 0
1's complement of 9 is 0 1 1 0
2's complement of 9 is 0 1 1 1
Now A = 1 0 1 0 ( total four digits)
B = + 0 1 1 1 (total four digits)
1 0 0 0 1 (total five digit)
In this case ignore the left most bit, so the final result is 0 0 0 1 ( 9 - 8 = +1)
Problem no 4: Find the value of 9 - 10
Binary value of 9 is 1 0 0 1
1's complement of 10 is 0 1 0 1
2's complement of 10 is 0 1 1 0
Now A = 1 0 0 1 ( total four digits)
B = + 0 1 1 0 (total four digits)
1 1 1 1 1 (total five digit)
In this case ignore the left most bit, so now the partial result is 1 1 1 1
And left most bit in 1 1 1 1 is 1 indicating that the result is negative and final result is in 2's complement form
The 2's complement of 1 1 1 1
1's complement of 1 1 1 1 is 0 0 0 0
2's complement of 1 1 1 1 is 0 0 0 0
+ 1
0 0 0 1
So the final result is -1 (9 -10 = -1)
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