Question

Convert 12/32 base 10 to binary number system

Answer 1

To convert the fraction \( \frac{12}{32} \) from base 10 to binary, we can first simplify the fraction:

\[
\frac{12}{32} = \frac{3}{8}
\]

Next, we can convert \( \frac{3}{8} \) to binary. We'll do this by separating the whole number and the fractional part.

1. The integer part is \( 0 \) (since \( \frac{3}{8} \) is less than 1).
2. The fractional part \( \frac{3}{8} \) can be converted to binary by multiplying by \( 2 \) repeatedly.

Here’s how it works:

- \( \frac{3}{8} \times 2 = \frac{6}{8} = 0.75 \) (integer part is \( 0 \))
- \( 0.75 \times 2 = 1.5 \) (integer part is \( 1 \))
- \( 0.5 \times 2 = 1.0 \) (integer part is \( 1 \))

Now we can stop here because we've reached an integer in the last step.

The integer parts collected from each step gives us the binary representation:

- From the first multiplication: \( 0 \)
- From the second multiplication: \( 1 \)
- From the third multiplication: \( 1 \)

Putting it together, \( \frac{3}{8} \) in binary is \( 0.011 \).

Thus, \( \frac{12}{32} \) in binary is:

\[
0.011_2
\]