Answer:
The answer is: 100011.001₂.
Explanation:
First, transform to binary the integer part: 35. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to 0:
- 35 ÷ 2 = 17 + 1;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
Now, construct the integer part base 2 representation, by taking the remainders starting from the bottom of the list:
Then, transform to binary the fractional part: 0.125. Multiply it repeatedly by 2, keeping track of each integer part of the results, until we get a fractional part that is equal to 0:
- 0.125 × 2 = 0 + 0.25;
- 0.25 × 2 = 0 + 0.5;
- 0.5 × 2 = 1 + 0;
Construct the fractional part base 2 representation by taking all the integer parts of the multiplying operations, starting from the top of the list.
0.125₁₀ = 0.001₂
Then you have:
35.125₁₀ = 100011.001₂
