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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