Question
Answer and Explanation
Converting the binary number 1.01 to base 10 involves understanding place values in both the integer and fractional parts of the binary number. Here's how it works:
Understanding Binary Place Values:
In binary (base-2), each digit's place represents a power of 2. To the left of the decimal, place values increase (2⁰, 2¹, 2², etc.). To the right, the values are fractional and decrease (2⁻¹, 2⁻², 2⁻³, etc.). So, for 1.01:
- The 1 to the left of the decimal point is in the 2⁰ place (which equals 1 in base-10).
- The 0 immediately after the decimal is in the 2⁻¹ place (which is 1/2 or 0.5 in base-10) - The 1 is in the 2⁻² position (which is 1/4 or 0.25 in base-10).
Step-by-Step Conversion:
1. Start with the digit to the left of the decimal point, so in '1.01', we look at '1':
1 2⁰ = 1 1 = 1
2. Then the fractional part after the decimal (0.01)
0 2⁻¹ = 0 (1/2) = 0
1 2⁻² = 1 (1/4) = 0.25
Combining:
Add these base-10 values together:
1 + 0 + 0.25 = 1.25
The Result
Therefore, the binary number 1.01 in base 10 is 1.25.
In conclusion, each digit is multiplied by its respective power of 2, then all products are summed to derive the decimal equivalent of any binary number, integer and fractional.