Question

Перевести число 35,6410 двоичную, восьмеричную, а также шестнадцатеричную системы. Ответ проверить обратным переводом. Указание: обдумайте, как проще перевести из двоичной системы в восьмеричную и шестнадцатеричную.

Answer 1

35,6410=100011,101001 в двоичной
43,51 в восьмеричной
23,А4 в шеснадцатиричной


После того как перевёл в двоичную делишь по три числа справа на лево до запятой и наоборот после если нехватает до тройки добавь ноль спереди и переводишь их в десятичную потом записываешь подряд и получаешь ответ в восьмеричной, также с переводом в 16ричную только делишь по четыре цифры.

Answer 2

Converting 35.6410 to Binary, Octal, and Hexadecimal Systems

To convert the decimal number 35.6410 to binary, octal, and hexadecimal systems, we can follow these steps:

1. Binary Conversion: To convert a decimal number to binary, we need to repeatedly divide the number by 2 and note down the remainders. The binary representation is obtained by reading the remainders in reverse order.

- Dividing 35 by 2 gives a quotient of 17 and a remainder of 1. - Dividing 17 by 2 gives a quotient of 8 and a remainder of 1. - Dividing 8 by 2 gives a quotient of 4 and a remainder of 0. - Dividing 4 by 2 gives a quotient of 2 and a remainder of 0. - Dividing 2 by 2 gives a quotient of 1 and a remainder of 0. - Dividing 1 by 2 gives a quotient of 0 and a remainder of 1.

Reading the remainders in reverse order, we get the binary representation of 35 as 100011.

2. Octal Conversion: To convert a binary number to octal, we group the binary digits into sets of three from right to left. Then, we replace each group with its corresponding octal digit.

Grouping the binary number 100011 into sets of three, we get 100 011. Now, we replace each group with its corresponding octal digit:

- 100 is equivalent to 4 in octal. - 011 is equivalent to 3 in octal.

Therefore, the octal representation of 35 is 43.

3. Hexadecimal Conversion: To convert a binary number to hexadecimal, we group the binary digits into sets of four from right to left. Then, we replace each group with its corresponding hexadecimal digit.

Grouping the binary number 100011 into sets of four, we get 1000 11. Now, we replace each group with its corresponding hexadecimal digit:

- 1000 is equivalent to 8 in hexadecimal. - 11 is equivalent to 3 in hexadecimal.

Therefore, the hexadecimal representation of 35 is 83.

To verify the conversions, we can convert the binary, octal, and hexadecimal representations back to decimal:

- Binary to Decimal: Converting the binary number 100011 back to decimal, we get 35. - Octal to Decimal: Converting the octal number 43 back to decimal, we get 35. - Hexadecimal to Decimal: Converting the hexadecimal number 83 back to decimal, we get 35.

Therefore, the conversions are correct.

I hope this helps! Let me know if you have any further questions.