A. 111000.101
B. 111101.001
C. 110111.100
D. 100101.101

Solution

A. 111000.101

Explanation

<p><span style="font-size: 14px;"><b>1. Convert the Integer Part (56) to Binary</b></span></p><p><span style="font-size: 14px;">Divide by 2 repeatedly:</span></p><ul><li><span style="font-size: 14px;">56 ÷ 2 = 28&nbsp; &nbsp;remainder 0&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">28 ÷ 2 = 14&nbsp; &nbsp;remainder 0&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">14 ÷ 2 = 7&nbsp; &nbsp; remainder 0&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">7 ÷ 2 = 3&nbsp; &nbsp; &nbsp;remainder 1&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">3 ÷ 2 = 1&nbsp; &nbsp; &nbsp;remainder 1&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">1 ÷ 2 = 0&nbsp; &nbsp; &nbsp;remainder 1</span></li></ul><p><span style="font-size: 14px;">Now, write remainders bottom to top:</span></p><p><span style="font-size: 14px;">56₁₀ = 111000₂</span></p><p><span style="font-size: 14px;"><b>2. Convert the Fractional Part (0.625) to Binary</b></span></p><p><span style="font-size: 14px;">Multiply by 2 repeatedly and take the integer part:</span></p><ul><li><span style="font-size: 14px;">0.625 × 2 = 1.25&nbsp; &nbsp; → 1&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">0.25 × 2&nbsp; = 0.5&nbsp; &nbsp; &nbsp;→ 0&nbsp;&nbsp;</span></li><li><span style="font-size: 14px;">0.5 × 2&nbsp; &nbsp;= 1.0&nbsp; &nbsp; &nbsp;→ 1</span></li></ul><p></p><p><span style="font-size: 14px;">So, 0.625₁₀ = .101₂</span></p><p><br></p><p><span style="font-size: 14px;"><b>Final Answer:</b></span></p><p></p><p><span style="font-size: 14px;">56.625₁₀ = 111000.101₂</span></p>