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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) 1 1 1 1 1 Carry bits
1 0 1 1 1 1
For example, let us add the binary numbers (101111)
2
and (10111) . + 1 0 1 1 1
2
1 0 0 0 1 1 0
Binary Subtraction
In binary subtraction, the 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. The rules for binary subtraction:
X Y X – Y
1 1
0 0 0 – 0 = 0 _____
0 (10) (10) (10) Borrow
0 – 1 = 1
0 1
(borrow 1, so that 10 – 1 = 1) 1 0 0 0
1 0 1 – 0 = 1 – 1 1 1
1 1 1 – 1 = 0 0 0 0 1
For example, let us subtract the binary number (111) from (1000) .
2 2
To Sum Up
The smallest piece of data that can be recognised and used by the computer is known
as a bit or a binary digit.
A number system is a way to express quantities used for counting, comparing amounts,
performing calculations and representing values.
A number system made up of ten symbols, 0 to 9, is known as the decimal number
system.
A number system made up of only two symbols, 0 and 1, is known as the binary
number system.
A number system made up of eight symbols, 0 to 7, is known as the octal number
system.
A number system made up of sixteen symbols, 0 to 9 and A to F, is known as the
hexadecimal number system.
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Number System

