The Floating-Point Format to Be Used in This Problem Is

question 8

Essay

The floating-point format to be used in this problem is an 8-bit IEEE 754 normalized format with 1 sign bit, 4 exponent bits, and 3 mantissa bits. It is identical to the 32-bit and 64-bit formats in terms of the meaning of fields and special encodings. The exponent field employs an excess- 7coding. The bit fields in a number are (sign, exponent, mantissa). Assume that we use unbiased rounding to the nearest even specified in the IEEE floating point standard.
(a) Encode the following numbers the 8-bit IEEE format:
(b) Perform the computation 1.011binary + 0.0011011binary showing the correct state of the guard, round and sticky bits. There are three mantissa bits.
(c) Decode the following 8-bit IEEE number into their decimal value: 1 1010 101
(d) Decide which number in the following pairs are greater in value (the numbers are in 8-bit IEEE 754 format):
(1) 0 0100 100 and 0 0100 111
(2) 0 1100 100 and 1 1100 101
(e) In the 32-bit IEEE format, what is the encoding for negative zero?
(f) In the 32-bit IEEE format, what is the encoding for positive infinity?
(1) 0.0011011binary
(2) 16.0decimal

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Definitions:

Fair Value

An estimated market value of an asset or liability based on current market conditions rather than historical cost.

Vesting Date

The date on which an employee gains full control over the benefits or stock options granted as part of their compensation package.

Remuneration Expense

Costs incurred by an organization to compensate its employees, including salaries, wages, bonuses, and benefits.

Vesting Period

The time period an employee must wait before gaining access to the employer's contributions in a pension plan or stock options.