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Let's start by addressing the question in the image. The problem involves converting numbers between binary and decimal systems.

Here is the breakdown of each conversion:

1. **(11110101)₂ to decimal:**

   To convert binary to decimal:
   \[
   1 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
   \]
   \[
   = 128 + 64 + 32 + 16 + 0 + 4 + 0 + 1 = 245
   \]
   So, \((11110101)_2 = 245_{10}\).

2. **(125)₁₀ to binary:**

   To convert decimal 125 to binary:
   \[
   125 ÷ 2 = 62 \text{ remainder } 1 \\
   62 ÷ 2 = 31 \text{ remainder } 0 \\
   31 ÷ 2 = 15 \text{ remainder } 1 \\
   15 ÷ 2 = 7 \text{ remainder } 1 \\
   7 ÷ 2 = 3 \text{ remainder } 1 \\
   3 ÷ 2 = 1 \text{ remainder } 1 \\
   1 ÷ 2 = 0 \text{ remainder } 1
   \]
   So, \(125_{10} = (1111101)_2\).

3. **(1001000)₂ to decimal:**

   Using the same method as before for binary to decimal conversion:
   \[
   1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 0 \times 2^0
   \]
   \[
   = 64 + 0 + 0 + 8 + 0 + 0 + 0 = 72
   \]
   So, \((1001000)_2 = 72_{10}\).

4. **(1100101)₂ to decimal:**

   \[
   1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
   \]
   \[
   = 64 + 32 + 0 + 0 + 4 + 0 + 1 = 101
   \]
   So, \((1100101)_2 = 101_{10}\).

5. **(100)₁₀ to binary:**

   To convert decimal 100 to binary:
   \[
   100 ÷ 2 = 50 \text{ remainder } 0 \\
   50 ÷ 2 = 25 \text{ remainder } 0 \\
   25 ÷ 2 = 12 \text{ remainder } 1 \\
   12 ÷ 2 = 6 \text{ remainder } 0 \\
   6 ÷ 2 = 3 \text{ remainder } 0 \\
   3 ÷ 2 = 1 \text{ remainder } 1 \\
   1 ÷ 2 = 0 \text{ remainder } 1
   \]
   So, \(100_{10} = (1100100)_2\).

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Would you like more details on any of these conversions or clarifications?

Here are 5 related questions you might find interesting:

1. How do you convert a fractional decimal number to binary?
2. What is the process for converting hexadecimal numbers to binary?
3. Can you explain how to perform arithmetic operations in binary (e.g., addition, subtraction)?
4. How is the two's complement system used to represent negative numbers in binary?
5. What is the significance of each bit in a binary number in relation to the power of two?

**Tip:** When converting from binary to decimal, always remember that each bit represents a power of two, starting from the rightmost bit at \(2^0\).

Convert the following binary numbers to decimal and decimal numbers to binary.

Learn how to convert binary numbers (e.g., (11110101)₂ and (1001000)₂) to decimal, and decimal numbers (e.g., 125₁₀ and 100₁₀) to binary with detailed solutions. This problem introduces key concepts of base systems, suitable for students in Grades 8-10.

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