Question

Convert (35.125)10 to binary

Answer 1

The answer is: 100011.001₂.

Step-by-step 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:

• 35₁₀ = 100011₂

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