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Binary Addition
Binary addition is similar to the addition of decimal numbers. In Binary Number System, when
the value of addition exceeds the value 1, say 10 or 11, then 1 is carried over to the left of the
current position. The rules for adding two binary digits are given below:
X Y X + Y
0 0 0 + 0 = 0
0 1 0 + 1 = 1
1 0 1 + 0 = 1
1 1 1 + 1 = 10 (carry 1)
For example, let us add the binary numbers (101111) and (10111) .
2
2
_____
1 1 1 1 1 Carry bits
1 0 1 1 1 1
+ 1 0 1 1 1
1 0 0 0 1 1 0
Binary Subtraction
In binary subtraction, binary number of lower value is subtracted from the binary number of
higher value. The following table explains the subtraction of digit Y from digit X. If Y is greater
than X, then 1 is borrowed from the next position. When the binary digit 0 borrows 1 from the
next most significant digit, it becomes 10.
X Y X – Y
0 0 0 – 0 = 0
0 – 1 = 1
0 1
(borrow 1, so that 10 – 1 = 1)
1 0 1 – 0 = 1
1 1 1 – 1 = 0
For example, let us subtract the binary number (111) from (1000) .
2 2
1 1
0 (10) (10) (10) _____ Borrow
1 0 0 0
– 1 1 1
0 0 0 1
Number System 13

