Let's convert each of the decimal numbers to their binary equivalents.

1. Converting $0.5$ to binary:

• Multiply $0.5 \times 2 = 1.0$
• The integer part is 1. So, the binary representation is 0.1.

2. Converting $0.25$ to binary:

• Multiply $0.25 \times 2 = 0.5$
• Multiply $0.5 \times 2 = 1.0$
• The binary representation is 0.01.

3. Converting $0.125$ to binary:

• Multiply $0.125 \times 2 = 0.25$
• Multiply $0.25 \times 2 = 0.5$
• Multiply $0.5 \times 2 = 1.0$
• The binary representation is 0.001.

4. Converting $0.625$ to binary:

• Multiply $0.625 \times 2 = 1.25$ → Integer part = 1
• Multiply $0.25 \times 2 = 0.5$ → Integer part = 0
• Multiply $0.5 \times 2 = 1.0$ → Integer part = 1
• The binary representation is 0.101.

Final Results:

1. $0.5 = 0.1_2$
2. $0.25 = 0.01_2$
3. $0.125 = 0.001_2$
4. $0.625 = 0.101_2$

Would you like any further details on the conversion process or have any questions?

Related Questions:

1. How do you convert decimal numbers greater than 1 to binary?
2. What is the binary equivalent of $0.75$?
3. How does the fractional binary representation work for repeating decimals?
4. Can you explain how negative decimals are represented in binary?
5. How can floating-point numbers be stored in binary using IEEE 754?

Tip: For binary fractions, each digit after the decimal represents a negative power of 2, like $2^{-1}, 2^{-2}, 2^{-3}, \ldots$.