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The second problem is that assembly language isn't portable. If you write an assembly-language program for the Intel 8080, it's not suitable for the Motorola 6800. You must rewrite the program in 6800 assembly language. This probably won't be as difficult as writing the original program because you've already solved the major organizational and algorithmic problems. But it's still a lot of work.

I explained in the last chapter how modern microprocessors have built-in machine-code instructions that do floating-point arithmetic. This is certainly convenient, but it doesn't go quite far enough. It would be preferable to abandon entirely those processor-dependent machine-code instructions that perform individual rudimentary arithmetic operations, and instead express multiple mathematical operations using a time-honored algebraic notation. Here's an example:

A x Sin (2 x PI + B) / C

where A, B, and C are numbers and PI is equal to 3.14159.

Well, why not? If such a statement were in a text file, it should be possible to write an assembly-language program that reads the text file and converts the algebraic expression to machine code.

If you needed to calculate such an algebraic expression only once, you could do it by hand or with a calculator. It's likely you're considering a computer solution because you need to calculate that expression with many different values of A, B, and C. For this reason, the algebraic expression will probably not appear in isolation. You should also consider some kind of context for the expression that allows it to be evaluated for different values.

What you're on the verge of creating here is known as a high-level programming language. Assembly language is considered a low-level language because it's very close to the hardware of the computer. Although the term high-level is used to describe any programming language other than assembly language, some languages are considered to be higher level than others. If you were the president of a company and you could sit at your computer and type in (or better yet, just prop your feet up and dictate), "Calculate all the profits and losses for this year, write up an annual report, print off a couple thousand copies, and send them to all our stockholders," you would be working with a very high-level language indeed! In the real world, programming languages don't come anywhere close to that ideal.

Human languages are usually the result of hundreds and thousands of years of complex influences, random changes, and adaptations. Even artificial languages such as Esperanto betray their origins in real language. High-level computer languages are, however, more deliberate conceptions. The challenge of inventing a programming language is quite appealing to some people because the language defines how a person conveys instructions to the computer. It was estimated in 1993 that there had been over 1000 high-level languages invented and implemented since the beginning of the 1950s.

Of course, it's not enough to simply define a high-level language (which involves developing a syntax to express all the things you want to do with the language); you must also write a compiler, which is the program that converts the statements of your high-level language to machine code. Like an assembler, a compiler must read through a source-code file character by character and break it down into short words and symbols and numbers. A compiler, however, is much more complex than an assembler. An assembler is simplified somewhat because of the one-to-one correspondence between assembly-language statements and machine code. A compiler usually must translate a single statement of a high-level language into many machine-code instructions. Compilers aren't easy to write. Whole books are devoted to their design and construction.

High-level languages have advantages and disadvantages. A primary advantage is that high-level languages are usually easier to learn and to program in than assembly languages. Programs written in high-level languages are