Question

I was reading somewhere that:

The smallest integer larger than lg N
is the number of bits required to
represent N in binary, in the same way
that the smallest integer larger than
log10 N is the number of digits
required to represent N in decimal.

The Java statement

for (lgN = 0; N > 0; lgN++, N /= 2) ; 

is a simple way to compute the
smallest integer larger than lg N

I maybe missing something here but how does the Java statement calculate the smallest integer larger than lg N?

Answer 1

Have any problem just tracing this on sample input?

step 1) N = 10, lgN = 0
step 2) N = 5,  lgN = 1
step 3) N = 2,  lgN = 2
step 4) N = 1,  lgN = 3
step 5) N = 0,  lgN = 4

lgN is 4 in the end. That’s the smallest integer larger than log(2, 10)