Consider a hypothetical 8 bit floating point machine representation with a sign bit, a 3 bit exponent, and a 4 bit mantissa (se1e2e3b1b2b3b4), where the exponent bias is 3 (add 3 to exponent of number to form machine representation). Recall that actual mantissa has 5 bits, since the leading 1 is not stored on the machine.

Systems Architecture
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Chapter8: Data And Network Communication Technology
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Consider a hypothetical 8 bit floating point machine representation with a sign bit, a 3 bit exponent, and a 4 bit mantissa (se1e2e3b1b2b3b4), where the exponent bias is 3 (add 3 to exponent of number to form machine representation). Recall that actual mantissa has 5 bits, since the leading 1 is not stored on the machine.

(a) What is the number ?≈2.718 in this 8-bit format?

(b) What is the number that (10100111)2 represents in this 8-bit format?

(c) What is the upper bound of the relative error when representing a real number in this 8-bit format?

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