====== 2. Integer and floating point number representation and operations ======
  * for lecturer: [[..:..:..:internal:tutorials:02:start|tutorial 2]]
===== Exercise outline =====

  - integer representation, addition, subtraction, multiplication, division
  - real number represetation (in IEEE 754)
  - 1st homework

===== What topics should I repeat before this exercise =====

  - logic operations (and, or, invert, rotation, ...)
  - two's complement code and IEEE 754.
  - to understand the program from the last class.

===== What shall we do on the second exercise =====

The aim of today's exercise is representation of real and integer numbers in computer and arithmetical operations with them.

===== Tasks =====
  - Integer addition and subtraction in two's complement representation
    * add and subtract two integer numbers. For example 5+(-6) and 5-(-6).
    * repeat the operations with different numbers and check your results with the computer program from the first exercise.
    * When the underflow and overflow can happen? How can we detect, that it had occured?
  - Integer multiplication
    * multiply two integers, For example 7*6.
    * is there any difference when multiplying negative numbers? (e.g. -7*6, (-7)*(-6), etc...) 
    * show how to speed-up the multiplier? (use many adders instead repetitively using one).
  - Integer division
    * divide integers 42/7, 43/7
    * does the algorithm change when we use negative numbers?
  - Real number representation (IEEE 754)
    * binary representation of real numbers (float - 32bit, double - 64bit)
    * show binary representation of -0.75. Check your result with program from the last exercise.
    * find decimal number for float binary number 0xC0A00000 in IEEE754.
    * explain who to add numbers 9.999*10^1 and 1.1610*10^(-1) in decimal representation. Assume that it is possible to store only 4 digits in mantisa and 2 digits in exponent.
      * Hint: 1) align numbers 2) addition 3) normalization 4) round numbers.
    * in binary representation add 0.5 and -0.4375
    * in decimal representation show multiplication of 1.110*10^10 * 9.200*10^(-5)
    * in binary representation multiply 0.5 and -0.4375

===== References =====

 * [[http://opensource.apple.com/source/gcc_os/gcc_os-1660/gcc/config/fp-bit.c|gcc/config/fp-bit.c]] - Implementation of float point operations with real numbers using fixed point arithmetic as used in [[http://gcc.gnu.org|GCC]] compiler. Used on processors without hardware floating point support.

/*  * [[courses:a0b36apo:solutions:02:start]]*/