Unraveling the Mystery of Binary Conversion

Have you ever wondered how to convert a decimal number into binary?

If so, let's explore the process of converting the decimal number 35.125 into binary.

Answer:

The answer is: 100011.001₂.

Understanding how to convert decimal numbers to binary can be quite fascinating. In this case, let's break down the conversion process of the decimal number 35.125 into binary:

Integer Part Conversion:

To begin, we convert the integer part of 35. Divide the number repeatedly by 2, keeping track of each remainder until we reach a quotient of 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

Constructing the integer part base 2 representation by taking the remainders from bottom to top gives us: 35₁₀ = 100011₂.

Fractional Part Conversion:

Next, we convert the fractional part of 0.125. Multiply it repeatedly by 2, keeping track of the integer parts of the results until we reach a fractional part of 0:

• 0.125 × 2 = 0 + 0.25
• 0.25 × 2 = 0 + 0.5
• 0.5 × 2 = 1 + 0

Constructing the fractional part base 2 representation by taking the integer parts in reverse order gives us: 0.125₁₀ = 0.001₂.

Combining the integer and fractional parts, we get the binary representation of 35.125 as 100011.001₂. This showcases the step-by-step process of converting a decimal number into binary, unveiling the magic behind the binary number system.