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

question 7

Essay

The floating-point format to be used in this problem is a normalized format with 1 sign bit, 3 exponent bits, and 4 mantissa bits. The exponent field employs an excess-4 coding. 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 in the above format:
(b) (1) 1.0binary
(c) (2) 0.0011011binary
(b) In one sentence for each, state the purpose of guard, rounding, and sticky bits for floating point arithmetic.
(c) Perform rounding on the following fractional binary numbers, use the bit positions in
italics to determine rounding (use the rightmost 3 bits):
(1) Round to positive infinity: +0.100101110binary
(2) Round to negative infinity: -0.001111001binary
(4) Unbiased to the nearest even: +0.100101100binary
(5) Unbiased to the nearest even: -0.100100110binary
(d) What is the result of the square root of a negative number?

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Definitions:

Price Ceiling

A maximum legal price that can be charged for a good or service, aimed at preventing prices from becoming too high.

Equilibrium Price

The market price at which the quantity of a good demanded equals the quantity supplied, leading to no excess supply or shortage.

Abolished

Refers to formally putting an end to a system, practice, or institution.

Government Involvement

Refers to the activities and interventions by the government in the market to regulate or support economic operations and social policies.