bit-manipulation

Bit Manipulation

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Bit masking

Get

set

clear

toggle

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Binary numbers

Binary numbers are base-2

101101 = 45

101101 = 45

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Addition

0110 + 0010 = 1000 or 6 + 2 = 8

0110 + 0010 = 1000 or 6 + 2 = 8

Add from right to left ,

If is 1+1 = 2 , becomes 0 and add 1 to next column (left)

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Subtraction

0110 - 0011 = 0011 or 6 - 3 = 3

0110 - 0011 = 0011 or 6 - 3 = 3

Subtract from right to left

If it is 0 - 1 , borrow from left

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Multiplication

00110101 = 1111 or 35 = 15

00110101 = 1111 or 35 = 15

0011 is the multiplicand

0101 is the multiplier

1. Multiply from right to left the multiplier digit to the mulitplicand digits

2. Make sure that each multiplied result is in it corresponding places

3. Sum the multiplied results

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Division

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AND

Bitwise AND Operator

&

Returns 1 if both the bits are 1 else 0.

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OR

Bitwise OR Operator

|

Returns 1 if either the bits are 1 else 0.

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NOT

Bitwise OR Operator

~

Inverse the bits

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XOR

Bitwise OR Operator

^

Returns 1 if only one of the bits is 1

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Left Shift

Bitwise left shift operator

<<

Shift bits to left and fills right with 0

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Shifting a single bit to the left by one place doubles its value

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Right Shift

Bitwise left shift operator

Shift bits to right and delete those values that fall off

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Shifting a single bit to the right by one place halfs its value

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Signed vs Unsigned numbers

Signed ( either positive or negative )

• Left most bit is the sign bit

  • 0 means positive

  • 1 means negative

Unsigned ( only positive )

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2’s complement

Why? Because using Sign-Magnitude method is only good for representing positive and negative numbers , and but does not work well in computating them(addition, subtraction)

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1. Write out the positive of number

2. Invert the bits , add 1

3. Add sign bit to front

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Negative number