Question

Перевести из двоичного системы счисления в десятичную число . Подробно

Answer 1

Converting Binary to Decimal

To convert a number from binary to decimal, you can use the positional notation method. Each digit in a binary number represents a power of 2, starting from the rightmost digit as 2^0, the next digit as 2^1, and so on. You multiply each digit by its corresponding power of 2 and sum them up to get the decimal equivalent.

Let's take the binary number 1001101.1101 as an example and convert it to decimal.

1. Write down the binary number: 1001101.1101.

2. Separate the whole number part from the fractional part, if any. In this case, the whole number part is 1001101 and the fractional part is 1101.

3. Convert the whole number part to decimal: - Start from the rightmost digit and assign powers of 2 to each digit, starting from 2^0. - Multiply each digit by its corresponding power of 2 and sum them up.

   1 * 2^6 + 0 * 2^5 + 0 * 2^4 + 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 77
   

Therefore, the whole number part 1001101 in binary is equal to 77 in decimal.

4. Convert the fractional part to decimal: - Start from the leftmost digit and assign negative powers of 2 to each digit, starting from -2^1. - Multiply each digit by its corresponding power of 2 and sum them up.

   1 * 2^-1 + 1 * 2^-2 + 0 * 2^-3 + 1 * 2^-4 = 0.8125
   

Therefore, the fractional part 1101 in binary is equal to 0.8125 in decimal.

5. Combine the whole number and fractional parts to get the final decimal equivalent: ``` 77 + 0.8125 = 77.8125 ```

Therefore, the binary number 1001101.1101 is equal to 77.8125 in decimal.