Example IV
What are the largest normalized floating-point numbers in single and double precision?
Single-precision representation:
Exponent–Bias = 254–127 = 127
(254 is the largest value for SP because 255 is reserved.)
Significand = 1.111...12 = almost 2
Value in decimal ≈ 2×2127 = 2128 ≈ 3.4028...×1038
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Double-precision representation:
Exponent–Bias = 2046–1023 = 1023
(2046 is the largest value for DP.)
Significand = 1.111...12 = almost 2
Value in decimal ≈ 2×21023 = 21024 ≈ 1.797610...×10308
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Question:
What is the smallest normalized single-precision floating-point number?