Question
Convert the binary (base-2) number 1001 to decimal (base-10).
A. 9
B. 10
C. 16
D. 17
Answers
GPT-4o mini
To convert the binary number \(1001\) to decimal, we can use the place value method. Each digit in the binary number represents a power of 2, starting from the rightmost digit, which is \(2^0\).
The binary number \(1001\) can be broken down as follows:
\[
1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
\]
Calculating each term:
- \(1 \times 2^3 = 1 \times 8 = 8\)
- \(0 \times 2^2 = 0 \times 4 = 0\)
- \(0 \times 2^1 = 0 \times 2 = 0\)
- \(1 \times 2^0 = 1 \times 1 = 1\)
Now, add all these values together:
\[
8 + 0 + 0 + 1 = 9
\]
Therefore, the decimal equivalent of the binary number \(1001\) is \(9\), which corresponds to option **A**.
The binary number \(1001\) can be broken down as follows:
\[
1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
\]
Calculating each term:
- \(1 \times 2^3 = 1 \times 8 = 8\)
- \(0 \times 2^2 = 0 \times 4 = 0\)
- \(0 \times 2^1 = 0 \times 2 = 0\)
- \(1 \times 2^0 = 1 \times 1 = 1\)
Now, add all these values together:
\[
8 + 0 + 0 + 1 = 9
\]
Therefore, the decimal equivalent of the binary number \(1001\) is \(9\), which corresponds to option **A**.