ELECTRONICS, PART THREE

Let's see, we left off with the teaser for numbering systems ...

You already know decimal, the one that has ten steps. It is what you use every day, the good old 0,1,2,3,4,5,6,7,8,9 digits. Binary only has two-steps, 0 and 1. This is useful in computers, which are very dumb. One and zero can represent on/off, open/closed, set/reset, high/low and so on. This forms the basis for all computing. The very CPU I am using now to type this uses those simple yes/no, pass/fail kind of decisions to handle the work I am doing. It keeps up with my two finger typing and at the same time it keeps up with various housekeeping like monitoring the I/O ports and keeping the Time-Of-Day. The only advantage a computer has over a human is that the computer is way faster: it can easily do a million things while a human (me) is mumblescratching around looking for a key on a keyboard. Of course, computers can't reason any better than a rock.

Binary is very inefficient. It takes seven bits of binary to represent one single character, say the letter, "A". The ASCII coding for "A" is 1000001. But because computers are so fast, this is not a drawback. In decimal 1000001 is 65, and in hexadecimal (which we will get to in a moment) it is 41₁₆.

You will note the subscript "16" after the 41. That is one way to indicate that the number is hexadecimal, also called hex. Otherwise you could not tell it from decimal in a lot of cases. You can also put a "h" after the number.

The binary system that all digital electronics use is based on uses powers-of-two, just like decimal uses powers-of-ten. So, the progression of powers of two: 1,2,4,8,16,32,64,128 etc. So the character "A" mentioned above, binary 1000001, means that there is a "1" in the 1 weighted position, which is 2 to the first power, and a "1" in the 64 weighted position, 2 to the seventh power.

Hexadecimal (and its older brother, octal), directly divides the binary into nibbles of 4 bits (or 3 for octal), in this case 41. Octal for the same binary number is 101. Hexadecimal and octal are more 'efficient' than decimal in computer work because they do not waste any binary space. Hex uses the letters A,B,C,D,E, and F to represent the numbers 10 through 15, or 1010 through 1111 binary.

Decimal, on the other hand, only has the digits 0 through 9. Enough of these numbers, they are putting me to sleep. Let's return to analog and digital ...