Question

Question 19 In representing the decimal number 11/8 in IEEE 754 representation, the 8-bit binary value of the exponent plus bias for single precision is 01111111 01111110 01111101 10000000

Answer 1

Answer

19) a.  01111111
13) d.  011 0000 0000 0000 0000 0000
12) b.  it can be placed anywhere in the number...
14) b.  10000.001
Converting 16.125 to binary
Convert decimal part first, then the fractional part
> First convert 16 to binary
Divide 16 successively by 2 until the quotient is 0
   > 16/2 = 8, remainder is 0
   > 8/2 = 4, remainder is 0
   > 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 10000
So, 16 of decimal is 10000 in binary
> Now, Convert 0.12500000 to binary
   > Multiply 0.12500000 with 2. Since 0.25000000 is < 1. then add 0 to result
   > Multiply 0.25000000 with 2. Since 0.50000000 is < 1. then add 0 to result
   > Multiply 0.50000000 with 2. Since 1.00000000 is >= 1. then add 1 to result
   > This is equal to 1, so, stop calculating
0.125 of decimal is .001 in binary
so, 16.125 in binary is 10000.001

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