~ Data Representation

How to represent negative numbers

So, we've looked at how to represent positive numbers. For instance a 10 (Binary) is a "2" in decimal. But what about negative numbers? How on earth do we represent those>? Let's look at the twos complement method to begin with and there is also sign and magnitude.

Video: Representing + and - numbers in Binary

Video:Sign and Magnitude

Adding Binary Fractions

The great insights of computer science

The philosopher of computing Bill Rapaport noted three Great Insights of Computer Science:

All the information about any computable problem can be represented using only 0 and 1 (or any other bistable pair that can flip-flop between two easily distinguishable states, such as "on/off", "magnetized/de-magnetized", "high-voltage/low-voltage", etc.).
  • Alan Turing's insight: there are only five actions that a computer has to perform in order to do "anything".
Every algorithm can be expressed in a language for a computer consisting of only five basic instructions:
  • move left one location;
  • move right one location;
  • read symbol at current location;
  • print 0 at current location;
  • print 1 at current location.
See also: Turing machine
  • Corrado Böhm and Giuseppe Jacopini's insight: there are only three ways of combining these actions (into more complex ones) that are needed in order for a computer to do "anything".
Only three rules are needed to combine any set of basic instructions into more complex ones:
  • sequence: first do this, then do that;
  • selection: IF such-and-such is the case, THEN do this, ELSE do that;
  • repetition: WHILE such-and-such is the case DO this.
Note that the three rules of Boehm's and Jacopini's insight can be further simplified with the use of goto (which means it is more elementary than structured programming).
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