Copyright © 2007, 2011, 2012 by Daniel B. Sedory
NOT to be reproduced in any form without Permission of the Author!
How PC Programs Work:
Whether you want to create your own programs or simply try to understand how others work, you must have a listing of all the basic Intel x86 Opcodes and a copy of Ralf Brown's famous Interrupt List (see the References section below for obtaining free downloads of both items). If you move on to C/C++ or Win32 Assembly (see below) programming for Windows®, you'll also need to know about Windows API calls!
"Hexa... What?" Well, that's hexa- (six)
plus decimal (ten), or sixteen.
It stands for the Base 16 Number System. Programmers often refer to
it as simply, Hex (which by itself should mean
only six, such as the number of sides that a "Hex wrench" has, but
it almost always means Hexadecimal if the subject is computer software rather
than hardware).
Just before FAT32 was invented, many people had hard drives that used 32 KiB clusters; with lots of wasted space on them. The space you save by using Windows™ 2000/XP with NTFS rather than FAT32 can be huge since the size of new drives has already reached triple digits of Gigabytes!
So, what does a Base 16 number system have to do with a machine that's based (
pun intended) on zeros
and ones?Do any of those numbers above look familiar to you, specifically the number 1024 and its multiples? It's more than just a coincidence that this is equal to the term we call a Binary Kilobyte (1024 bytes, or 2 to the power of 10 or 1 KiB). The 2 Kib, 4 Kib and 16 Kib multiples of this Binary number should now be evident in the Table above. 10,000 Hex (FFFFh + 1) is equivalent to 64 Binary KB (65,536 bytes, or 2 to the power of 16) which is the largest size a true .COM program* can have.
After laying some groundwork from the past, we'll return to these observations and answer that important question in the box above! Hopefully you'll enjoy the following commentary on highlights from the history of computing.
A Quick Look at the Amazing History of Computers
Over half a century ago, hot, room-sized machines built with vacuum tubes and relays were already using the same concepts we still use today to carry out instructions on numbers stored as "bits" (Binary digits) in structures known as registers. Today, even our hand-held programmable calculators could blow away those old computers in speed if not in results (number of digits). And the registers have shrunk from the size of handfuls of light bulbs to a space so tiny you need an electron microscope to see it; yet they still continue to add, subtract and compare bits by the same logical methods already known long before those now archaic machines could have been built.
Programs were often stored and fed into those first computers from patterns of holes punched into a roll of paper tape (Punched Tape). This idea came from an earlier device called the teletype (or teletypewriter or teleprinter), which used a seven-bit code we now call ASCII to send alphanumeric data over wires. Essentially this same bit code or expansions upon it, such as Unicode, are still used to store data on a PC. Designed for communications, the original code included control characters to signal the start of, success, failure, and end of transmissions. The ASCII code 7, was used to ring a real bell at a distant station, thus it is often abbreviated as "bell" in an ASCII chart. Programs now use it to beep a computer's speaker!Seven bits gives us a total of 128 different codes in the standard ASCII character set. That's 64 + 32 + 16 + 8 + 4 + 2 + 1 or 127, plus the zero. At a much later date, companies such as IBM® and Apple® introduced their own Extended ASCII character sets; which were eventually followed by Unicode.
Read the full page at: http://thestarman.pcministry.com/asm/hexawhat.html
Instead of making its own Disk Operating System, IBM® paid a little software company to put together a DOS for their new IBM Personal Computers. But, IBM did not pay for exclusive rights to any future uses of this DOS. And when that little company (called Microsoft®) made some changes and started selling MS-DOS™ to anyone, it wasn't long until a flood of "AT clones" and "IBM - compatibles" spread across the globe! Microsoft and Intel® made a fortune selling the essential software and hardware that made up a PC, but IBM simply acted like its usual "big blue" self over the losses in home and small business sales. I'm sure that IBM now wishes they had done things differently, but perhaps that's what they deserved for making a calculated decision to promote Microsoft's DOS instead of an 8086 version of CP/M by Gary Kildall (which later became Digital Research DOS). And in spite of what you may read elsewhere, Gary never 'lost out' to Bill Gates due to any personal differences or missed meetings! It was simply a business decision by IBM; which appears to have been done on purpose since IBM's DOS could only be used on their machines, whereas Gary's OS was almost machine independent. It's a little known fact (these days) that IBM actually licensed both DOS and CP/M-86 for their PC, but you had to special order CP/M-86 rather than having it come at a much lower price with most PCs as IBM's DOS did; that was clearly a business decision on the part of IBM!
Bits, Bytes, Characters and Words
Data in these new microcomputers was contained in 8-bit units called "bytes" (a combination of the word bit and to bite; a 4-bit unit is often called a "nibble"
).
IBM® later added an extended-ASCII character set for their
PCs, which doubled the size from 128 to 256 codes. Inside the
Processor itself (the CPU), there were also registers of 16-bit
lengths. The machine code which ran the CPU could have instructions
of this size too, or even larger, arriving at the CPU in a number of successive
bytes. It was around this time, that the term "word" took
on its usual meaning of two eight-bit bytes. So,
how did they manipulate such large binary numbers without making too many
mistakes?Long before this, programmers regularly used a convenient method to handle large binary numbers in either 3-bit or 4-bit groupings. Most people find it quite easy to see what decimal numbers are represented by only three bits; for example, 101 is 5, 011 is 3, etc. If we use the 3-bits at a time method to convert the binary number 111000101000 into groups of 3-bit decimal digits, we obtain: 7 0 5 0. "If you needed to turn this into an Octal (Base 8) number, what more would you need to do?" Nothing! The digits 7050 are the Octal equivalent of this Binary number; it's almost too simple. But to convert either of them into Decimal is a lot more difficult for most of us; yet it's quite often unnecessary for a programmer to do so.
Not long after computers needed to be programmed, the actual machine code for the computer instructions was replaced by mnemonics (first m is silent when pronouncing this word; it essentially means abbreviations). Three or four letters (at first), were used in what was called the Assembly Language for a particular CPU; thus, today we have the x86 Assembly code (in various forms) for Intel-based computers. It was also possible to use more than one base numeration for writing data in these Assembly languages, so programmers made sure their Assemblers [the programs which convert Assembly language into a particular machine code] could understand Octal as well as Binary numbers.Well, what about Hexadecimal? The same Binary number above, grouped into four bits at a time, will give us the Hex numerals, E28. Now we're finally getting to the bottom of that important question above; and the main reason I wanted to write this essay.
The maximum number a four-bit Binary can represent is 15. Exactly the same as a single Hex digit. And if you sum up the next four higher bits in a Binary number having eight bits, for example, the ones in 11110000, you'll get 16+32+64+128 = 240, or simply 15 times 16. And the next four bits beyond that will give you 15 times 256, or 3840.
Let's compare the differences between grouping the Binary digits in sets of fours (for Hexadecimal) and threes (for Octal) in a more graphic manner :