====== Math 753/853 exercises 3: 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.