Sure, let’s convert the binary number [tex]\( 11001_2 \)[/tex] to its base ten equivalent step-by-step.
1. Identify the binary number: The given binary number is [tex]\( 11001_2 \)[/tex].
2. Write down the positional values: Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is the least significant bit). So, the positions from right to left are:
- [tex]\( 2^0 \)[/tex]
- [tex]\( 2^1 \)[/tex]
- [tex]\( 2^2 \)[/tex]
- [tex]\( 2^3 \)[/tex]
- [tex]\( 2^4 \)[/tex]
3. Assign the binary digits to these positions: Write the binary number under these positional values:
[tex]\[
\begin{array}{ccccc}
2^4 & 2^3 & 2^2 & 2^1 & 2^0 \\
1 & 1 & 0 & 0 & 1 \\
\end{array}
\][/tex]
4. Calculate the values of each digit in the binary number:
- [tex]\( 1 \times 2^4 = 1 \times 16 = 16 \)[/tex]
- [tex]\( 1 \times 2^3 = 1 \times 8 = 8 \)[/tex]
- [tex]\( 0 \times 2^2 = 0 \times 4 = 0 \)[/tex]
- [tex]\( 0 \times 2^1 = 0 \times 2 = 0 \)[/tex]
- [tex]\( 1 \times 2^0 = 1 \times 1 = 1 \)[/tex]
5. Sum these values to get the base ten equivalent:
[tex]\[
16 + 8 + 0 + 0 + 1 = 25
\][/tex]
Therefore, the binary number [tex]\( 11001_2 \)[/tex] converted to base ten is:
[tex]\[
\boxed{25}
\][/tex]
