Give the binary equivalent of the decimal number of 19.9 (assume fixed point, no more than...

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)

Expert Solution

10011.111001

Explanation:
-------------
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

venereology answered 2 years ago

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