Decimal Equivalent of Binary Number (11010.101)2

To find the decimal equivalent of a binary number, we need to understand the place value system in binary and decimal systems.

Binary Place Values:
In a binary number, each digit represents a power of 2 starting from right to left. The rightmost digit represents 2^0, the next digit represents 2^1, the next represents 2^2, and so on.

Decimal Place Values:
In a decimal number, each digit represents a power of 10 starting from right to left. The rightmost digit represents 10^0, the next digit represents 10^1, the next represents 10^2, and so on.

Converting the Integer Part:
The integer part of the binary number (11010)2 can be converted to decimal by multiplying each digit with the corresponding power of 2 and adding them together.

(11010)2 = (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)
= 16 + 8 + 0 + 2 + 0
= 26

Converting the Fractional Part:
The fractional part of the binary number (0.101)2 can be converted to decimal by multiplying each digit with the corresponding negative power of 2 and adding them together.

(0.101)2 = (1 * 2^-1) + (0 * 2^-2) + (1 * 2^-3)
= 0.5 + 0 + 0.125
= 0.625

Combining the Integer and Fractional Part:
To find the decimal equivalent of the entire binary number (11010.101)2, we combine the decimal values of the integer and fractional parts.

Decimal equivalent = Integer part + Fractional part
= 26 + 0.625
= 26.625

Therefore, the correct answer is option C) 26.625.