https://file.aiquickdraw.com/mathbot/file/1727414587544pz4pka2k.jpg

Let's solve the problems from the image step by step, as they involve converting numbers between different number systems.

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### 1. Convert \( 1100111_2 \) to Decimal
**Binary to Decimal conversion:**

The binary number \( 1100111_2 \) can be expanded as:

\[
1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0
\]

This gives us:

\[
64 + 32 + 0 + 0 + 4 + 2 + 1 = 103_{10}
\]

Thus, \( 1100111_2 = 103_{10} \).

---

### 2. Convert \( 475_8 \) to Decimal
**Octal to Decimal conversion:**

The octal number \( 475_8 \) can be expanded as:

\[
4 \times 8^2 + 7 \times 8^1 + 5 \times 8^0
\]

This gives us:

\[
4 \times 64 + 7 \times 8 + 5 \times 1 = 256 + 56 + 5 = 317_{10}
\]

Thus, \( 475_8 = 317_{10} \).

---

### 3. Convert \( A9F_{16} \) to Decimal
**Hexadecimal to Decimal conversion:**

The hexadecimal number \( A9F_{16} \) can be expanded as:

\[
A \times 16^2 + 9 \times 16^1 + F \times 16^0
\]

Here, \( A = 10 \) and \( F = 15 \), so we have:

\[
10 \times 16^2 + 9 \times 16^1 + 15 \times 16^0 = 10 \times 256 + 9 \times 16 + 15 \times 1
\]

This gives us:

\[
2560 + 144 + 15 = 2719_{10}
\]

Thus, \( A9F_{16} = 2719_{10} \).

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Would you like more details on any of the conversions, or do you have any questions?

### Related Questions:
1. What are the steps for converting from decimal to binary?
2. How can you convert a decimal number to hexadecimal?
3. Why is base-2 used in computers and digital systems?
4. How do you convert octal numbers to hexadecimal without using decimal as an intermediate?
5. What is the process of converting fractions from binary to decimal?

### Tip:
When converting from any base to decimal, break down each digit as a multiple of the base raised to the power of its position, starting from 0 on the right.

Convert the following Binary, Octal, and Hexadecimal numbers to Decimal.

Learn how to convert Binary (1100111_2), Octal (475_8), and Hexadecimal (A9F_16) numbers to Decimal with step-by-step solutions. Understand the key formulas used in positional number systems. Suitable for high school students.

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