In this Binary Arithmetic Representation,we concerned on this topics:- Binary Addition,Binary Subtraction,Binary Multiplication and Binary ...
In this Binary Arithmetic Representation,we concerned on this topics:-Binary Addition,Binary Subtraction,Binary Multiplication and Binary Division.So starting with Binary Addition.
Example 1: 11101.11 + 11010.10
1 1 1 0 1 . 1 1
1 1 0 1 0 . 1 0
-------------------------------------------
1 1 1 0 0 0 . 0 1
-------------------------------------------
Example 1: 111000.01+1111101.10
1 1 1 0 0 0 . 0 1
1 1 1 1 1 0 1 . 1 0
---------------------------------------------------------
1 0 1 1 0 1 0 1 . 1 1
---------------------------------------------------------
Binary Subtraction:-
Example 1:-1110-1001
1 1 1 0
1 0 0 1
-----------------
o 1 0 1
-----------------
Example 2(using 2's Complement):-
When 1st value is lesser than 2nd value then we use 2's Complement.
->0101-1010
First we take 1's complement of bigger value=0101
Then we takes 2's complement
0101
+1
----------
0110
----------
then, (add)
0 1 1 0
0 1 0 1
-----------------
1 0 1 1 =-5
-----------------
Binary Multiplication:-
Example 1:-
1 1 0 1 1 0 1
* 1 0 1
------------------------------------------------
1 1 0 1 1 0 1
0 0 0 0 0 0 0 X
1 1 0 1 1 0 1 X X
-------------------------------------------------
1 0 0 0 1 0 0 0 0 1
-------------------------------------------------
Example 2:-
1 1 0 1 1 0 1
* 1 1 1
------------------------------------------------
1 1 0 1 1 0 1
1 1 0 1 1 0 1 X
1 1 0 1 1 1 0 X X
-------------------------------------------------
1 0 1 1 1 1 1 1 1 1
-------------------------------------------------
Binary Division:-
10011
--------------------------
11|1 1 1 0 1 1
1 1
-------------
1 0 1
1 1
---------
1 0
---------
Binary Addition:-
A | B | A+B | Cout |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
Example 1: 11101.11 + 11010.10
1 1 1 0 1 . 1 1
1 1 0 1 0 . 1 0
-------------------------------------------
1 1 1 0 0 0 . 0 1
-------------------------------------------
Example 1: 111000.01+1111101.10
1 1 1 0 0 0 . 0 1
1 1 1 1 1 0 1 . 1 0
---------------------------------------------------------
1 0 1 1 0 1 0 1 . 1 1
---------------------------------------------------------
Binary Subtraction:-
A | B | A-B | Bout |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 0 |
Example 1:-1110-1001
1 1 1 0
1 0 0 1
-----------------
o 1 0 1
-----------------
Example 2(using 2's Complement):-
When 1st value is lesser than 2nd value then we use 2's Complement.
->0101-1010
First we take 1's complement of bigger value=0101
Then we takes 2's complement
0101
+1
----------
0110
----------
then, (add)
0 1 1 0
0 1 0 1
-----------------
1 0 1 1 =-5
-----------------
Binary Multiplication:-
Example 1:-
1 1 0 1 1 0 1
* 1 0 1
------------------------------------------------
1 1 0 1 1 0 1
0 0 0 0 0 0 0 X
1 1 0 1 1 0 1 X X
-------------------------------------------------
1 0 0 0 1 0 0 0 0 1
-------------------------------------------------
Example 2:-
1 1 0 1 1 0 1
* 1 1 1
------------------------------------------------
1 1 0 1 1 0 1
1 1 0 1 1 0 1 X
1 1 0 1 1 1 0 X X
-------------------------------------------------
1 0 1 1 1 1 1 1 1 1
-------------------------------------------------
Binary Division:-
10011
--------------------------
11|1 1 1 0 1 1
1 1
-------------
1 0 1
1 1
---------
1 0
---------
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