The limits of a fixed number of bits

In this lesson

Explain the limitations of representing data in binary when the number of available bits is fixed, and describe what happens when a value will not fit.

What it covers

• N bits gives 2 to the n distinct patterns and not one more - the whole video rests on this
• For an unsigned whole number that means a range of 0 to 2 to the n, minus 1
• A fixed field width limits how many different THINGS can be labelled, not only how big a number can be - addresses, characters in a set, states of a switch
• What happens at the edge: the value does not fit, and something has to give
• The trade-off in both directions: more bits buys range but costs storage and memory; fewer bits saves space but loses values you will one day want
• The general principle stated once, cleanly: a bit you did not spend is a value you cannot have

Key words

On the specification