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:

Cathode

The electrode from which electrons exit a device or where positive ions enter.

Voltaic Pile

A group of voltaic cells connected together to form a battery.

Alessandro Volta

An Italian physicist known for inventing the battery in the 1800s, leading to the development of the first source of continuous electrical current.

Electricity

A form of energy resulting from the existence of charged particles, such as electrons or protons, either statically as an accumulation of charge or dynamically as a current.