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: