Binary addition
Counting is the process of adding 1 to
the present number to get the next number. In decimal number system
counting start from 0 and proceeds like this 0,1,2,3,4,5,6,7,8,9 .
After nine we have no more symbols left, so we write 10. This one
represent a carry to the tens position.
Like this binary system's count process
can also be represented like this 0,1,10,11,100 ….
Based on the above idea we construct a
half adder table to represent the addition of binary numbers.
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a
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b Sum Carry
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||
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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1
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0
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1
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1
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1
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1
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Here we have not used carry , but
consider the examples below.
11+01=100
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Carry
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1
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1
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Augend
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1
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1
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Addend
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0
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1
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Sum
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1
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0
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0
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101+001=110
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Carry
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0
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1
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|
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Augend
|
1
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0
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1
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Addend
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0
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0
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1
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Sum
|
1
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1
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0
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These two examples show that
addition between two numbers include addition between three bits; the
carry bit and the bits of the two numbers to be added. We can
construct a addition table having these three values.
-
ab Carry Sum Carry to next position0000000110010100110110010101011100111111
In short rules for addition are
0+0=0
1+0=1
0+1=1
1+1=0 , and a carry to the next
significant digit
