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updated
24 / 6 / 2006

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
NUMBER SYSTEM, BINARY ADDITION AND SUBTRACTION AND TWO's COMPLEMENT METHOD
 
NUMBER SYSTEM
 
1 - Decimal Number System (10)
2 - Binary Number System (2)
3 - Octal Number System (8)
4 - Hexa Decimal Number System (16)
 
1 - Decimal Number System (10)
It takes the value from 0 - 9. Other numbers are made up from these digits. In base 10 systems, the place values are 10^5 , 10^4 , 10^3 , 10^2 , 10^1 , 10^0 . (i.e) 100000, 10000, 1000, 100, 10, 1.
 
2 - Binary Number System (2)
It just uses two numbers. It takes the digits 1 and 0. Other numbers are made up from a series of these numbers. The place values are 2^5, 2^4, 2^3, 2^2, 2^1,2^1. (i.e) 32, 16, 8, 4, 2, 1.
 
3 - Octal Number System (8)
It uses eight numbers. They are 0, 1, 2, 3, 4, 5, 6, 7. The place values are 8^3, 8^2, 8^1, 8^0. (i.e) 512, 64, 8, 1.
 
4 - Hexa Decimal Number System (16)
It uses 16 numbers. They are 0 - 9, A, B, C, D, E, F. The place values are 16^3, 16^2, 16^1, 16^0. (i.e) 4096, 256, 16, 1.
 
 
BINARY ADDITION
 

1 + 1 = 10
0 + 1 = 1
1 + 0 = 1
0 + 0 = 0
1 + 1 + 1 = 11
1 + 1 + 1 + 1 = 100

 
 
BINARY SUBTRACTION

 

1 - 1 = 0
1 - 0 = 1
0 - 0 = 0
0 - 1 = 1 (after borrowing one from the next place)

 
 
TWO's COMPLEMENT METHOD
 

Eg: 115 - 75

2 |115
2 |57 - 1
2 |28 - 1
2 |14 - 0
2 |7 - 0
2 |3 - 1
# |1 - 1

= 1110011

 

2 |75
2 |37 - 1
2 |18 - 1
2 |9 - 0
2 |4 - 1
2 |2 - 0
# |1 - 0

= 1001011

1001011

0110100
#####+1
----------
0110101
1110011 +
----------
10101000

= 01010002

 
First change the decimal to binary, and then take the answer you got in the second one (that is; 1001011 (75)) and then change the 0's to 1's and 1's to 0's. So you get 0110100. Then do binary addition of 1. When you get the answer (0110101) do binary addition again with the first answer (1110011). Finaly remove the '1' u get at the left of the answer and note it down.
 
 
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