Question

Convert 43.2 base 8 to binary, base 3, decimal and hexadecimal. Any fractions that do not terminate should be truncated to 4 digits in the fractional part.

Answer 1

The conversion of 43.2 base 8 yields the following results: binary -
`\(100011.001\), base 3 - \(11200.2\), decimal - \(35.125\),` and hexadecimal -
`\(23.2\).`

Step-by-step explanation:

To convert a number from one base to another, we start by converting it to the decimal system. For base 8 to decimal, we use the positional value of each digit. In this case, \
`(43.2_8\) becomes \(4 * 8^1 + 3 * 8^0 + 2 * 8^(-1)\),` resulting in the decimal representation of
`\(35.125\).`

Next, we convert the decimal number to binary, base 3, and hexadecimal. The integer part is converted using repeated division by the base, while the fractional part is converted using repeated multiplication by the base. The truncated binary representation of
`\(35.125\) is \(100011.001\)`, the base 3 representation is
`\(11200.2\)`, and the hexadecimal representation is
`\(23.2\).`

In summary, the conversion of
`\(43.2_8\)` to binary, base 3, decimal, and hexadecimal yields the respective results of
`\(100011.001\), \(11200.2\), \(35.125\), and \(23.2\)`. These conversions involve the application of fundamental principles of positional notation and the use of appropriate methods for each target base.