1. Give the binary equivalent of the decimal number of 11.77 (assume fixed point, no more...

1. 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)

Solutions

Expert Solution

1011.110001

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

venereology answered 2 years ago

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