Final Answer:
The result of adding 0.101011₂ (binary) and 0.00012₂ (binary) is equal to 0.101131₂ in binary, which is equivalent to approximately 0.413818359375 in decimal.
Step-by-step explanation:
To calculate the sum, align the binary numbers by their decimal points:
0.101011
+ 0.00012
__________
0.101131
Adding the binary numbers results in 0.101131₂. To convert this binary sum to decimal, each digit's positional value is calculated:
(0 * 2^0) + (1 * 2^(-1)) + (1 * 2^(-2)) + (1 * 2^(-3)) + (3 * 2^(-4)) + (1 * 2^(-5))
= 0 + 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125
≈ 0.76875
Therefore, the decimal equivalent of the binary sum 0.101131₂ is approximately 0.76875.
This process involves the conversion of binary fractions to their decimal equivalents by summing the positional values of each digit. It demonstrates the conversion between different number bases and the precision required when working with binary arithmetic.