The Floor Of The Log2 Of A Number

In mathematics and computer science the floor function is the function that takes as input a real number and gives as output the greatest integer less than or equal to denoted or similarly the ceiling function maps to the least integer greater than or equal to denoted or.

The floor of the log2 of a number.

First by using a scientific calculator calculating what log2 2096 is by. Log base 2 calculator finds the log function result in base two. Floor of base two is nothing but the floor of a binary number. 3 32 log 2096 11 027 and then from here i can see that that floor 11 and ceiling 12 so ceiling x floor x 1 but when i review my answer i am incorrect usually due to how i calculate log2 2096.

Now if i have a number in binary by scanning all bits one by one i can determine the index of the msb but it will take me order n time. Let s see examples floor 10 15 3 15 in binary floor 2 110 decimal equivalent 6 100 decimal equivalent 4 so to do this function first convert it into binary then take only the left most 1 and put the rest as 0 s. Floor of base 10 gives floor of decimals. Some say int 3 65 4 the same as the floor function others say int 3 65 3 the neighbouring integer closest to zero or just throw away the 65.

The int function short for integer is like the floor function but some calculators and computer programs show different results when given negative numbers. We only need to use logarithm property to find the value of log n on arbitrary base r. I e where k can be any anything which for standard log functions are either e or 10. If there is a number in binary in a n bit system then the floor log of the number is defined as the index of the msb of the number.

Math floor x parameters x a number. Calculate the log2 x logarithm of a real number find log base 2 of a number. O log n auxiliary space. The floor function returns the largest integer that is smaller than or equal to x.

Because floor is a static method of math you always use it as math floor rather than as a method of a math object you created math is not a constructor. O log n if the stack size is considered during recursion otherwise o 1 using inbuilt log function.