Question

Find the binary and hexadecimal equivalents of 0.0875, multiplying this decimal number by 2 and 16, respectively. Stop the process if you notice a repeating pattern to the left of the decimal point.

Answer 1

To determine binary and hexadecimal equivalents of 0.0875, multiply it repeatedly by 2 for binary and by 16 for hexadecimal, each time carrying over the fractional part, until a repeating pattern is observed or the desired precision is achieved.

Step-by-step explanation:

To find the binary and hexadecimal equivalents of the decimal number 0.0875 by multiplying by 2 and 16, respectively, you'd follow these steps:

1. Multiply 0.0875 by 2:
2. 0.0875 × 2 = 0.175
3. Keep the 0.175 as the new value.
4. Multiply 0.175 by 2:
5. 0.175 × 2 = 0.35
6. Keep the 0.35 as the next value.
7. Continue this process until you notice a repeating pattern or you've reached sufficient precision for your needs. In this case, there is no repeating pattern immediately.

For hexadecimal:

1. Multiply 0.0875 by 16:
2. 0.0875 × 16 = 1.4
3. The whole number 1 becomes a part of the hexadecimal value, and the decimal 0.4 is carried over to the next multiplication.
4. Multiply 0.4 by 16:
5. 0.4 × 16 = 6.4
6. The whole number 6 becomes a part of the hexadecimal value, and you would carry over the 0.4 again to the next multiplication if needed.
7. Notice the repeating pattern of 0.4 when multiplied by 16, which would lead to a recurring hexadecimal number.

It is important to convert the whole number part of each multiplication result into binary or hexadecimal notation as you go and then continue the process with the fractional part.