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1. (16.67 pts) What would be the IEEE 754 single precision floating point representation of n

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1. (16.67 pts) What would be the IEEE 754 single precision floating point representation of n =

-76543210.98765432101234 × 1018? For explanation, I want you to document the steps your perform, in this order: (1) What is n in decimalfixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 25 bits following thebinary point; (3) What is the normalized binary number, written in the form 1.bbbbb…bbb × 2e, storing 25 bits followingthe binary point? (4) What are the 23 mantissa bits, after the bits in bit positions -24, -25, … are eliminated usingthe round to nearest, ties to even mode; exclude the 1. part which is not stored; (5) What is the biased exponent indecimal and in binary? (6) Write the 32-bits of the number in the order: s e m; and (7) Write the final answer as an 8-hexdigit number.

2. (16.67 pts) What decimal floating point number does this big-endian IEEE 754 single precision number represent: n= 0x6C84_3175? For explanation, I want you to document the steps you perform, in this order: (1) What is n inbinary; (2) What is the value of the sign bit; What does this value signify about the final number; (3) What are thebinary and decimal values of the biased exponent; (4) What is the binary value of the mantissa, with the 1. partpreceding the binary point? (5) What is the decimal value of the unbiased exponent; (6) What is the decimal value ofthe mantissa, with the leading 1. part? (7) What is the final decimal real number, written in the form [-]d.ddddddddddddddd × 10e where d represents a decimal digit 0-9 and there is an optional leading negative sign. Write exactly 15digits after the decimal point (even if they are 0’s) and round the final 15th digit up or down as required based on thevalue of the 16th digit (16th digit 5 round down; otherwise, round up).

3. (16.67 pts) What would be the IEEE 754 double precision floating point representation of 1.32487359893280124981233898124124 × 10-17. For explanation, I want you to document the steps you perform, in this order: (1) What is n indecimal fixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 110 bitsfollowing the binary point); (3) What is the normalized binary number, written in the form 1.bbbbb…bbb × 2e, storing54 bits following the binary point) (4) What are the 52 mantissa bits, after the bits in bit positions -53, -54, … areeliminated using the round to nearest, ties to even mode; exclude the 1. part; (5) What is the biased exponent indecimal and in binary? (6) Write the 64-bits of the number in the order: s e m; and (7) Write the final answer as a 16-hexdigit number.

 
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