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To convert the binary number \( 110001_2 \) into its decimal (base 10) equivalent, we can break it down by assigning powers of 2 to each digit.

Starting from the rightmost digit:
\[
110001_2 = 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
\]

Now, let's calculate each term:
\[
1 \times 2^5 = 32
\]
\[
1 \times 2^4 = 16
\]
\[
0 \times 2^3 = 0
\]
\[
0 \times 2^2 = 0
\]
\[
0 \times 2^1 = 0
\]
\[
1 \times 2^0 = 1
\]

Now, sum all the results:
\[
32 + 16 + 0 + 0 + 0 + 1 = 49
\]

Thus, the decimal (base 10) equivalent of \( 110001_2 \) is \( 49 \).

Would you like further details or explanations on this? Here are some related questions for further exploration:

1. How do you convert other binary numbers to decimal?
2. What is the general formula for converting any base to decimal?
3. How would you convert the decimal number 49 back to binary?
4. What are the steps to convert a binary fraction to decimal?
5. How does binary addition work in computer systems?

**Tip:** In binary conversion, each digit represents a power of 2, starting from the right (least significant bit) to the left (most significant bit).

Convert the following base 2 numeral to a base 10 numeral: 110001

Learn how to convert the binary number 110001 (base 2) to its decimal (base 10) equivalent. This example covers key concepts in number systems and explains the step-by-step method to break down a binary number. Suitable for students in Grades 6-8.

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