Question

Give the binary equivalent of the decimal number of 11.77 (assume fixed point, no more than 6 bits left and right of the decimal point)

Answer 1

1011.110001

Explanation:
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Converting 11.77 to binary
Convert decimal part first, then the fractional part
> First convert 11 to binary
Divide 11 successively by 2 until the quotient is 0
   > 11/2 = 5, remainder is 1
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1011
So, 11 of decimal is 1011 in binary
> Now, Convert 0.77000000 to binary
   > Multiply 0.77000000 with 2. Since 1.54000000 is >= 1. then add 1 to result
   > Multiply 0.54000000 with 2. Since 1.08000000 is >= 1. then add 1 to result
   > Multiply 0.08000000 with 2. Since 0.16000000 is < 1. then add 0 to result
   > Multiply 0.16000000 with 2. Since 0.32000000 is < 1. then add 0 to result
   > Multiply 0.32000000 with 2. Since 0.64000000 is < 1. then add 0 to result
   > Multiply 0.64000000 with 2. Since 1.28000000 is >= 1. then add 1 to result
0.77 of decimal is .110001 in binary
so, 11.77 in binary is 1011.110001
Answer: 1011.110001