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Bitwise Operations

What are bitwise operations?

Bitwise operations modify the pattern of bits in an object. Computers use binary numbers. A binary number consists of one or more digits, which represent two different states, such as on/off.

An example of a binary number looks like this:

10010

The first digit on the RIGHT side of the number is in the one's column. The second digit from the right is in the two's column, then comes the four's column, the eight's column, the sixteen's column and so on. Each column contains a "bit", or binary digit.

16 8 4 2 1

This example binary number, "10010", converted to a decimal number, evaluates like this.

168421

10010

16 * 1 = 16

8 * 0 = 0

4 * 0 = 0

2 * 1 = 2

1 * 0 = 0

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total = 18 in decimal numbers

It is possible to operate on the bits using BOOLEAN operators.

AND

The AND operator will set a bit only if both input bits are set.

'Bitwise AND

'This operation sets a bit only if

'both inputs have the bit set.

print 7 and 11 ' yields 3

'16 8 4 2 1 '

'-------------- '

' 0 0 1 1 1 ' 7 in binary

' 0 1 0 1 1 ' 11 in binary

' ^ ^ ' These are the place values where both numbers are 1.

' ' Hence, 2 + 1 = 3

The OR operator will set a bit if either input bit is set.

'Bitwise OR

'This operation sets a bit if

'either input has the bit set.

print 7 or 11 ' yields 15

'16 8 4 2 1 '

'-------------- '

' 0 0 1 1 1 ' 7 in binary

' 0 1 0 1 1 ' 11 in binary

' ^ ^ ^ ^ ' These are the place values where either number has a 1.

' ' Hence, 8 + 4 + 2 + 1 = 15

XOR

The Bitwise XOR operation sets a bit only if exactly one of the inputs has the bit set.

'Bitwise XOR

'This operation sets a bit only if

'exactly one of the inputs has the bit set.

print 7 xor 11 ' yields 12

'16 8 4 2 1 '

'-------------- '

' 0 0 1 1 1 ' 7 in binary

' 0 1 0 1 1 ' 11 in binary

' ^ ^ ' These are the place values where exactly one of the

' ' numbers has a 1. Hence, 8 + 4 = 12