How to read binary

If you are going to work with computers, you are going to be exposed to binary numbering.  There’s no way around this, as the base 2 (binary) math system is the basic language used in all computing, from the lowliest 8-bit to the most advanced 128-bit systems.  The “bit”, is, itself, the most basic part of binary counting.  In computing 8 bits produce one byte, or octet, which can be any number between 0-255, with 0 acting as a definite number as well as the equivalent of nil, or nothing.  Since every operation in a computer can ultimately be reduced to a true/false, or yes/no equation, binary is language of choice, with the only two numbers available being 0, or 1.

For people, the common counting system is decimal, or base 10, arguably because the earliest discovered counting method were the ten fingers available on hands.  The base number is how high you count before starting over at the next numeric place.  Computers don’t have fingers to start with, and have evolved around the concept that either something is, or it is not.  While they also use the hexadecimal numbering system, binary is much more commonly used.

It is important to remember that in binary 10000000 is a value of 1, not 10 million, a full octet, or byte is equal to 255, and represented by 11111111.  For most computing needs, the counting ends at a byte, although this is a matter of comprehension, not of actual truth. In actuality, the counting continues indefinitely, with each new number place being equal to a maximum of twice the preceding maximum.  In order to keep it simple we will only look at counting in binary up to the size of a single byte.

The following list outlines the first 8 numeric places in binary:
10000000=001= the only values allowed here are 0 and 1
01000000=002=2*1 (1 is maximum preceding value)
00100000=004=2*2 (2 is the maximum preceding value)
00010000=008=2*4 (4 s the max perceding value)
00001000=016=2*8 (8 is max preceding value)
00000100=032=2*16(16 is max preceding value)
00000010=064=2*32(32 is max preceding value)
00000001=128=2*64(64 is the max preceding value)

Once we’ve counted as high as 128, we can go back through the place list again for a another full 127, giving 8 1’s the total value of 255, and with the original plave value of 0, we have a total of 256 possible numbers in 8 numeric places of code.

A full octet is 11111111, which is equal to 2^8 or 255. Each place value is raised to the power of 2 for its full value.  This can be very confusing to grasp, but only because we have learned the use only the decimal system our entire lives.  In actuality, binary is a very logical (yes or no) method of counting.  For instance, assume that 1 is the basic number, the next numeric place can have a total of no more than 2*1 or twice the max value of previous places. The next numeric place can have a maximum value of twice the value of numeric places which precede it, etc.  It works exactly the way that base 10 works, but with the maximum value before adding a multiplier is 2, rather than 10. if the third place contains a 1, then that number is equal to 4, because the maximum available from all of the preceding places is 2.

Article written by MyComputerAid.com