Question

Convert the following numbers to binary.  Do not be concerned with normalization or the hidden bit for the purpose of this assignment.

(PLEASE SHOW STEPS SO I CAN EASILY UNDERSTAND. THANK YOU.)

58.4298095703125 calculated to eleven binary digits to the right of the decimal.

33.4021 calculated to eleven binary digits to the right of the decimal.

39.875 calculated to eleven binary digits to the right of the decimal.

Answer 1

STEPS TO CONVERT FRACTIONAL DECIMAL TO BINARY

A) Convert the integral part of decimal to binary equivalent

1. Divide the decimal number by 2 and store remainders in array.
2. Divide the quotient by 2.
3. Repeat step 2 until we get the quotient equal to zero.
4. Equivalent binary number would be reverse of all remainders of step 1.

B) Convert the fractional part of decimal to binary equivalent

1. Multiply the fractional decimal number by 2.
2. Integral part of resultant decimal number will be first digit of fraction binary number.
3. Repeat step 1 using only fractional part of decimal number and then step 2.

C) Combine both integral and fractional part of binary number.

Let's take an example for n = 4.47 k = 3

Step 1: Conversion of 4 to binary
1. 4/2 : Remainder = 0 : Quotient = 2
2. 2/2 : Remainder = 0 : Quotient = 1
3. 1/2 : Remainder = 1 : Quotient = 0

So equivalent binary of integral part of decimal is 100.

Step 2: Conversion of .47 to binary
1. 0.47 * 2 = 0.94, Integral part: 0
2. 0.94 * 2 = 1.88, Integral part: 1
3. 0.88 * 2 = 1.76, Integral part: 1

So equivalent bianry of fractional part of decimal is .011

Step 3: Combined the result of step 1 and 2.

Final answer can be written as:
100 + .011 = 100.011

Hence, following the same steps, the answers are:

a) 58.4298095703125₁₀ = 111010.01101110000₂

b) 33.4021₁₀ = 100001.01100110111₂

c) 39.875 = 100111.11100000000₂