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====== Math 753/853 exercises 4: floating point numbers ====== **1.** Based on 9/7/2016's lecture material, what range of integers should a 16-bit integer type represent? Check your answer by running ''typemin(Int16)'' and ''typemax(Int16)'' in Julia. **2.** Same as problem 1 for 32-bit integers. **3.** The standard 32-bit floating-point type uses 1 bit for sign, 8 bits for exponents, and 23 bits for the mantissa. * What is machine epsilon for a 32-bit float? * How many digits of accuracy does the mantissa have? * What are the minimum and maximum exponents, in base 10? **4.** The standard 16-bit floating-point type uses 1 bit for sign, 5 bits for exponents, and 10 bits for the mantissa. What size error do you expect in a 16-bit computation of 9.4 - 9 - 0.4? Figure out how to do this 16-bit calculation in Julia and verify your expectation. **5.** Find the roots of $x^2 - 4x + 6^{-28} = 0$ to four significant digits.
