Question

youre visiting a computer science building at a college, and theyre so excited itd be fun to display all the room numbers in binary (from going to room 11). what room number should you look for on the door of room 101? type the room number without any spaces.

Explanation:

Step1: Understand the pattern

The room numbering is in binary (base 2) and we need to convert the binary number 101 to decimal (base 10). The formula for converting a binary number \( b_{n}b_{n - 1}\dots b_{1}b_{0} \) to decimal is \( \sum_{i = 0}^{n}b_{i}\times2^{i} \).

Step2: Apply the formula

For binary number 101, we have:

• The right - most digit (i = 0): \( 1\times2^{0}=1\times1 = 1 \)
• The middle digit (i = 1): \( 0\times2^{1}=0\times2 = 0 \)
• The left - most digit (i = 2): \( 1\times2^{2}=1\times4 = 4 \)

Now, sum these values: \( 4 + 0+1=5 \)

Answer:

5