S5-2.1 Data Representation & Computer Arithmetic

Work through these

• Basic structure of computers and functional units

  The map of the machine before any detail: what the units are and how they talk. Come back to this item when a later topic feels like it is floating free of anything physical.

• Fixed point representation of numbers

  How numbers live in a register, and the conventions that decide what a bit pattern means. Everything in the next four items depends on getting this straight first.

• Digital arithmetic algorithms for addition and subtraction

  The arithmetic you already know, done the way hardware does it. Working an example on paper with real bit patterns is the difference between recognising the algorithm and being able to use it.

• Multiplication using Booth's algorithm

  The centrepiece of this topic, because it shows arithmetic as hardware rather than mathematics: it spots runs of ones and replaces many additions with one subtraction and one addition. Work it by hand or it will not stick.

• Division using restoring and non-restoring algorithms

  Two ways to divide, differing in what they do when the trial subtraction goes negative. The non-restoring version is faster for the reason its name gives, and tracing both on the same numbers makes that obvious.

• Floating point representation and the IEEE standards

  Why floating point comparisons betray you in every language you will ever write in. This item has a life well beyond the examination, so it is worth more than the two lines it takes up here.