Question

Give the binary equivalent of the decimal number of 19.9 (assume fixed point, no more than 6 bits left and right of the decimal point(show work)

Answer 1

10011.111001

Explanation:
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Converting 19.9 to binary
Convert decimal part first, then the fractional part
> First convert 19 to binary
Divide 19 successively by 2 until the quotient is 0
   > 19/2 = 9, remainder is 1
   > 9/2 = 4, remainder is 1
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10011
So, 19 of decimal is 10011 in binary
> Now, Convert 0.90000000 to binary
   > Multiply 0.90000000 with 2. Since 1.80000000 is >= 1. then add 1 to result
   > Multiply 0.80000000 with 2. Since 1.60000000 is >= 1. then add 1 to result
   > Multiply 0.60000000 with 2. Since 1.20000000 is >= 1. then add 1 to result
   > Multiply 0.20000000 with 2. Since 0.40000000 is < 1. then add 0 to result
   > Multiply 0.40000000 with 2. Since 0.80000000 is < 1. then add 0 to result
   > Multiply 0.80000000 with 2. Since 1.60000000 is >= 1. then add 1 to result
0.9 of decimal is .111001 in binary
so, 19.9 in binary is 10011.111001
Answer: 10011.111001