Corman exercice :Random(a, b)

I don't understand the answer of this exercise , especially why they take

n = [log(b - a +1 )] ?!!

I think n = ceil(log2(b))

here is the exercices :

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Describe an implementation of RANDOM(a, b) that only makes calls to RANDOM (0, 1) .

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and the answer :

1: n = [lg(b − a + 1)] 
2: Initialize an array A of length n
3: while true do
4:    for i = 1 to n do
5:       A[i] = RANDOM(0, 1)
6:    end for
7:    if A holds the binary representation of one of the numbers in a through
b     then
8:          return number represented by A
9:    end if
10: end while

link of page : http://sites.math.rutgers.edu/~ajl213/CLRS/CLRS.html

Thanks.