Final Answer:
The octal equivalent of the binary number 101110101.1101 is 555.54.
Step-by-step explanation:
To find the octal equivalent of the binary number 101110101.1101, we first need to convert it to its decimal equivalent. The binary number 101110101.1101 can be split into two parts: the integer part (101110101) and the fractional part (1101). To convert the integer part to decimal, we use the positional notation, where each digit's place value is a power of 2. Starting from the right, the place values are 2⁰, 2¹, 2², and so on. Therefore, the decimal equivalent of the integer part is calculated as follows:
(1 * 2⁸) + (0 * 2⁷) + (1 * 2⁶) + (1 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰) = 357
To convert the fractional part to decimal, we use the positional notation again, but this time with negative powers of 2. The decimal equivalent of the fractional part is calculated as follows:
(1 * 2⁻¹) + (1 * 2⁻²) + (0 * 2⁻³) + (1 * 2⁻⁴) = 0.8125
Now, add the decimal equivalents of the integer and fractional parts:
357 + 0.8125 = 357.8125
Finally, convert the decimal number 357.8125 to octal. The whole number part (357) is divided by 8 successively to obtain the octal equivalent, and the fractional part (0.8125) is multiplied by 8 successively to obtain the octal equivalent. Combining the results, we get the octal equivalent of 101110101.1101 as 555.54.