Question

Переводите числа из десятичной системы счисления в двоичную, восьмеричную, шестнадцатеричную. 369, 3269; 83.72; 596.103; 1658. Сделайте пожалуйста с полным решением)

Answer 1

Я еще 2 сделала, не знаю как вложить..(

Answer 2

Converting Decimal Numbers to Binary

To convert decimal numbers to binary, you can use the following steps:

1. Divide the decimal number by 2. 2. Write down the remainder (0 or 1). 3. Divide the quotient obtained in step 1 by 2 again. 4. Repeat steps 2 and 3 until the quotient becomes 0. 5. Write down the remainders in reverse order to get the binary representation.

Let's apply these steps to the given decimal numbers:

1. 369: - Dividing 369 by 2 gives a quotient of 184 and a remainder of 1. - Dividing 184 by 2 gives a quotient of 92 and a remainder of 0. - Dividing 92 by 2 gives a quotient of 46 and a remainder of 0. - Dividing 46 by 2 gives a quotient of 23 and a remainder of 0. - Dividing 23 by 2 gives a quotient of 11 and a remainder of 1. - Dividing 11 by 2 gives a quotient of 5 and a remainder of 1. - Dividing 5 by 2 gives a quotient of 2 and a remainder of 1. - 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. - Writing down the remainders in reverse order gives the binary representation: 101110001.

2. 3269: - Dividing 3269 by 2 gives a quotient of 1634 and a remainder of 1. - Dividing 1634 by 2 gives a quotient of 817 and a remainder of 0. - Dividing 817 by 2 gives a quotient of 408 and a remainder of 1. - Dividing 408 by 2 gives a quotient of 204 and a remainder of 0. - Dividing 204 by 2 gives a quotient of 102 and a remainder of 0. - Dividing 102 by 2 gives a quotient of 51 and a remainder of 0. - Dividing 51 by 2 gives a quotient of 25 and a remainder of 1. - Dividing 25 by 2 gives a quotient of 12 and a remainder of 1. - Dividing 12 by 2 gives a quotient of 6 and a remainder of 0. - Dividing 6 by 2 gives a quotient of 3 and a remainder of 0. - Dividing 3 by 2 gives a quotient of 1 and a remainder of 1. - Dividing 1 by 2 gives a quotient of 0 and a remainder of 1. - Writing down the remainders in reverse order gives the binary representation: 110011001101.

Converting Decimal Numbers to Octal

To convert decimal numbers to octal, you can use the following steps:

1. Divide the decimal number by 8. 2. Write down the remainder. 3. Divide the quotient obtained in step 1 by 8 again. 4. Repeat steps 2 and 3 until the quotient becomes 0. 5. Write down the remainders in reverse order to get the octal representation.

Let's apply these steps to the given decimal numbers:

1. 369: - Dividing 369 by 8 gives a quotient of 46 and a remainder of 1. - Dividing 46 by 8 gives a quotient of 5 and a remainder of 6. - Dividing 5 by 8 gives a quotient of 0 and a remainder of 5. - Writing down the remainders in reverse order gives the octal representation: 561.

2. 3269: - Dividing 3269 by 8 gives a quotient of 408 and a remainder of 5. - Dividing 408 by 8 gives a quotient of 51 and a remainder of 0. - Dividing 51 by 8 gives a quotient of 6 and a remainder of 3. - Dividing 6 by 8 gives a quotient of 0 and a remainder of 6. - Writing down the remainders in reverse order gives the octal representation: 6355.

Converting Decimal Numbers to Hexadecimal

To convert decimal numbers to hexadecimal, you can use the following steps:

1. Divide the decimal number by 16. 2. Write down the remainder. 3. Divide the quotient obtained in step 1 by 16 again. 4. Repeat steps 2 and 3 until the quotient becomes 0. 5. Write down the remainders in reverse order to get the hexadecimal representation.

For the decimal numbers provided, let's apply these steps:

1. 369: - Dividing 369 by 16 gives a quotient of 23 and a remainder of 1. - Dividing 23 by 16 gives a quotient of 1 and a remainder of 7. - Dividing 1 by 16 gives a quotient of 0 and a remainder of 1. - Writing down the remainders in reverse order gives the hexadecimal representation: 171.

2. 3269: - Dividing 3269 by 16 gives a quotient of 204 and a remainder of 5. - Dividing 204 by 16 gives a quotient of 12 and a remainder of 12 (C in hexadecimal). - Dividing 12 by 16 gives a quotient of 0 and a remainder of 12 (C in hexadecimal). - Writing down the remainders in reverse order gives the hexadecimal representation: CCC.

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