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1. Binary Addition, Subtraction ,
Multiplication and division

2. Binary addition:-
A B Sum Carry
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
Binary subtraction:-
A B Difference Borrow
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

3. Add the following binary numbers:
1. (1001)2 and (0101)2
2. (101.01)2 and (1101.10)2
Subtract the following binary numbers:
1. (0110)2 from (1010)2
2. (01011)2 from (11011)2

4. Binary Multiplication:-
A B Output
0 0 0
0 1 0
1 0 0
1 1 1
Binary Division:-
A B Output
0 1 0
1 1 1
Division by zero is meaning less

5. Solve the following binary multiplication
1. (101)2 and (11)2
2. (1011)2 and (1001)2
Solve the following division
1.(11001) by (101)
2. (110000) by (100)

6. 1’s complement:-
The 1’s complement of binary number is
obtained by changing each 0 to 1 and each 1 to
0. both the numbers complement each other.
If one of these number is positive , the other will
be negative with same magnitude and vice
versa.
2’s complement:-
If 1 is added to 1’s complement of a number
then it will obtain the 2’s complement of the
number.

7. Subtraction using 1’s complement
a) Subtraction of smaller number from a larger
number:-
1. Calculate the 1’s complement of a smaller
number.
2. add the 1’s complement to the larger
number.
3. If carry comes in the MSB , remove the
carry and add it to the result.

8. Subtraction using 1’s complement
b) Subtraction of larger number from a smaller
number:-
1.Calculate 1’s complement of a larger
number.
2. Add 1’s complement in smaller number
3. The result will be in 1’s complement form.
Calculate 1’s complement of final value and
assign –ve sign to the result.

9. Advantages of using 1’s complement
subtraction
1. This can be easily obtained by simply
inverting each bit in the number
2. This subtraction can be done with an binary
adder. Thus ,it is useful in arithmetic logic
circuits.

10. Subtraction using 2’s complement
a) Subtraction of smaller number from a larger
number:-
1. Calculate the 2’s complement of a smaller
number.
2. add the 2’s complement to the larger
number.
3. If carry comes in the MSB , discard the
carry .

11. Subtraction using 2’s complement
b) Subtraction of larger number from a smaller
number:-
1.Calculate 2’s complement of a larger
number.
2. Add 2’s complement in smaller number
3. The result will be in 2’s complement form.
Calculate 2’s complement of final value and
assign –ve sign to the result.

12. Unsigned and signed numbers
Unsigned numbers:-
Numbers without any positive and negative
sign.
Represents only magnitude

13. Sign magnitude numbers:-
In binary number system, both +ve and –ve values are
possible.
In this , we use 0’s and 1’s to represent every number.
The representation of number is known as signed
number.
0+ve number
1 -ve number.
Eg:- +7=0111
-7=1111
This kind of representation for signed numbers is
called as signed magnitude representation.

14. Different methods for the representation of
binary signed numbers
1. Sign magnitude form
2. 1’s complement form
3. 2’s complment form