Find Next and previous power of two of a given number
Next power of two
Example(1):
input: 22
output: 32 ( as 32 is 2^5)
Example(2):
input: 54
output: 64 (as 64 is 2^6)
Previous power of two
Example(1):
input: 22
output: 16
Example(2):
input: 54
output: 32
We can solve this problem using bit manipulation easily.
Just have a look on the binary representation of the number which is a power of 2.
power of 2 Binary Representation
1 1
2 10
4 100
8 1000
16 10000
32 100000
64 1000000
128 10000000
As we can see every number have only their left most bit set (i.e 1) and rest are unset (i.e 0).
Finding previous power of 2
If we somehow, can unset all bits except the left most bit in a binary representation of number we will get previous power of two of the given number.
Example:
Number Binary representation previous power of two
7 111 100 (i,e 4)
25 11001 10000 (i.e 16)
95 1011111 1000000 (i,e 64)
We will use Bitwise AND ( & ) operation to clear bits.
Here is Algorithm to get previous power of 2 of n,
step 1: n = n & n-1
step 2: if n is power of two , n is our desired result,go to step 3.
else go to step 1.
step 3: print n and stop
Explanation:
let n = 27 ( 11011 in binary)
n-1 = 26 ( 11010 in binary)
n&n-1 = 26
as 26 is not a power of 2 so we will repeat above step again
new n = 26
n = 26 ( 11010 in binary)
n-1 = 25 ( 11001 in binary)
n&n-1 = 24 ( 11000 in binary)
as 24 is not a power of 2 so we will repeat above step again
new n=24
n = 24 ( 11000 in binary)
n-1 = 23 ( 10111 in binary)
n&n-1 = 16 ( 10000 in binary)
as 16 is a power of 2 so this is our answer
Finding next power of Two
To get next power of two, all we have to do is to find a binary number greater than the given number having only left most bit set.
We can use left shift operator ( << )to generate a number having only its left most bit set.
Left shift operation example:
1 << 5
This means that shift 1 left by 5 place
1 in binary is represented as 1
so after shifting 1 by 5 place left,
output will be 100000 ( i.e 32 in decimal)
5 << 2
This means that shift 5 left by 2 place
5 in binary is represented as 101
so after shifting it by 2 place to left,
output will be 10100 ( i.e 20 in decimal)
Note: In each shift right most bit will be set to 0;
Program:
Output
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