Книга: Introduction to Microprocessors and Microcontrollers

The only problem with binary

The only problem with binary is that we find it so difficult and make too many errors. There is little point in designing microprocessors to handle binary numbers at high speed and with almost 100% accuracy if we are going to make loads of mistakes putting the numbers in and reading the answers.

From our point of view, binary has two drawbacks: the numbers are too long and secondly they are too tedious. If we have streams and streams of ones and zeros we get bored, we lose our place and do sections twice and miss bits out.

The speed of light in m/s can be written in denary as 299792459₁₀ or in binary as 10001110111100111100001001011₂. Try writing these numbers on a sheet of paper and we can be sure that the denary number will be found infinitely easier to handle. Incidentally, this binary number is less than half the length that a modern microprocessor can handle several millions of times a second with (almost) total accuracy.

In trying to make a denary number even easier, we tend to split it up into groups and would write or read it as 299 792 459. In this way, we are dealing with bite-sized portions and the 10 different digits ensure that there is enough variety to keep us interested. We can perform a similar trick with binary and split the number into groups of four bits starting from the right-hand end as we do with denary numbers.

1 0001 1101 1110 0111 1000 0100 1011

Already it looks more digestible.

Now, if we take a group of four bits, the lowest possible value is 0000₂ and the highest is 1111₂. If these binary numbers are converted to denary, the possibilities range from 0 to 15.

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