Question

1. (16.67 pts) What would be the IEEE 754 single precision floating point representation of n = -76543210.9876543210 1234 \times 10^{18}? For explanation, I want you to document the steps your perform, in this order: (1) What is n in decimal fixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 25 bits following the binary point; (3) What is the normalized binary number, written in the form $1.bbbbb...bbb \times 2^e$, storing 25 bits follow- ing the binary point? (4) What are the 23 mantissa bits, after the bits in bit positions -24, -25, ... are eliminated using the round to nearest, ties to even mode; exclude the 1. part which is not stored; (5) What is the biased exponent in decimal 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.

          1. (16.67 pts) What would be the IEEE 754 single precision floating point representation of n = -76543210.9876543210
1234 \times 10^{18}? For explanation, I want you to document the steps your perform, in this order: (1) What is n in decimal
fixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 25 bits following the
binary point; (3) What is the normalized binary number, written in the form $1.bbbbb...bbb \times 2^e$, storing 25 bits follow-
ing the binary point? (4) What are the 23 mantissa bits, after the bits in bit positions -24, -25, ... are eliminated using
the round to nearest, ties to even mode; exclude the 1. part which is not stored; (5) What is the biased exponent in
decimal 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.

1. (16.67 pts) What would be the IEEE 754 single precision floating point representation of n = -76543210.9876543210
1234 ×10^18? For explanation, I want you to document the steps your perform, in this order: (1) What is n in decimal
fixed point form (ddd.ddddd); (2) What is n in binary fixed point form (bbb.bbbb), storing the first 25 bits following the
binary point; (3) What is the normalized binary number, written in the form 1.bbbbb...bbb × 2^e, storing 25 bits follow-
ing the binary point? (4) What are the 23 mantissa bits, after the bits in bit positions -24, -25, ... are eliminated using
the round to nearest, ties to even mode; exclude the 1. part which is not stored; (5) What is the biased exponent in
decimal 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.

Added by April S.

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