Problem: If N, written in base 2, is 11000, the integer immediately preceding N, written in base 2, is:
Answer Choices:
A. 10001
B. 10010
C. 10011
D. 10110
E. 10111
Solution:
Method I. N−1=110002−1=1⋅24+1⋅23+0⋅22+0⋅2+0−1
∴N−1=1⋅24+0⋅23+1⋅22+1⋅2+(2−1)=101112
Method II. N=110002=2410 and 24_{10}-1=23_
Since 23_{10}=10111_{2}, N-1=10111_