Floating-Point Examples (Cont.)


Example V
What are the largest normalized floating-point numbers in single and double precision?

Answer:
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
0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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 ≈ 1.79769...×10308
0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Question: What is the smallest normalized single-precision floating-point number?

Answer:   in positive value     in negative value


Exponent–Bias = 10    Significand = 10