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Microcode: Electronic Building Blocks For Calculators

Last Update: January 22, 2003 -- THE HP REFERENCE

Hewlett Packard Personal Calculator Digest
Vol. 3, 1977
pp 4-6


Just as DNA can be called the building blocks of the human organism. Microcode can be called the building blocks of the electronic calculator.

But, while the way the human organism works is determined by heredity, the way an electronic calculator works is determined by the highly personal--and even idiosyncratic--creative impulses of a programming specialist.

The principles of programming can be learned, of course. But anyone who has programmed his own calculator quickly discovers that techniques may vary widely from person to person.

Consider the challenge faced by the professional programmer When you press the key labeled SIN, for example, you expect the calculator to display the sine of the value you have keyed into it--and presto, it does. But in that less-than-a-second interval between keystroke and display, the calculator has executed an internal program of about 3500 steps. And it does this according to the highly individualistic microcode that the programmer has created.

The development of microcode in Hewlett-Packard personal calculators began with the development developments of the microprocessor in the HP-35--and not coincidentally, since both were developed by the same Hewlett-Packard engineer.

It is the microprocessor that determines the "language" of the internal microcode. If you are familiar with computer languages such as BASIC, FORTRAN, and COBOL, you know that these languages structure the way you write your program on the computer. You can only do what the language lets you do.

The microprocessor is similar to the computer. It provides a language that a clever engineer can then build into a function on the keyboard.

The original HP-35 microprocessor has remained essentially unchanged through the years and is the heart of the new HP-19C and HP-29C. Compared with computer processors, the binary-coded decimal microprocessor is very simple it does not handle byte data well, but is, in fact, specially designed for 10-digit floating point numbers (See figure 1.). The resulting microcode language most closely resembles machine language, which is programming at as most basic level.

Most microprocessors use 8-bit instructions and two or three instructions are usually combined to perform one operation. The beauty of HP's calculator microcode is that 10-bit instructions are used and each usually performs a complete operation by itself.

The language's strongest point is its robust arithmetic section of 37 instructions combined with eight field-select options. The field-select options allow the program to apply the instruction to any word-select portion of the register (See figure 2.).

The language is also designed to use very little storage; only seven registers were used in the HP-35 of which five were user registers. This is done to reduce costs and to save valuable space. For the design engineer it means that he must accomplish all of his miracles within the program itself.

Based on warranty card analysis and other market research, parameters regarding the desired function set and price are given to the design engineer. It is his job then to determine the specific functions for the calculator and to attempt to fit them in the allotted memory. Price is an important factor to the engineer because it directly influences the amount of memory he has to work with.

Only after several months of hard work writing and compacting microcode will he know if the function set will fit. If it is not possible, the product may be redefined at a higher price with greater performance to increase the available memory. More likely however, the engineer will be forced to pare functions until his program fits.

To give you an idea of how much memory is required, the HP-35 used three pages of 256 instructions each. Each page required a separate ROM read-only memory.

The HP-45 originally took six pages of instructions. But about that time the quad ROM was developed, which, as its name implies, was the equivalent of four conventional ROM'S. So for the HP-45, two quad ROM's were used. It was in the leftover two pages that an enterprising designer placed the celebrated HP-45 clock. Later calculators, listed below, continued to use quad ROM's.

Note: 1 quad = 1024 instructions or 4 pages of 256 instructions each. -Rick-

Writing the microcode is where the designer's personality is stamped indelibly on the Calculator. While it is true that the fundamental algorithms for commuting the complex mathematical functions found in HP personal calculators have remained essentially the same since the HP-35, the individual code is substantially different.

+---------------------------------------------------------------------+
| NUMBER   REGISTER REPRESENTATION                                    |
|                                                                     |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|   23.4   | 0 | 2 | 3 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |  |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|                                                                     |
|            a                                                        |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|  -123.   | 9 | 1 | 2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |  |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|                                                                     |
|                                                                   b |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|  .002    | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 9 | 9 | 7 |  |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|                                                                     |
|          a. A "9" in the sign position indicates a negative number. |
|          b. Exponents are kept in 10's complement form.             |
|                                                                     |
+---------------------------------------------------------------------+
|  Figure 1. All numbers in registers are in scientific notation with |
|  the mantissa portion of the number left justified in the mantissa  |
|  portion of the register.                                           |
+---------------------------------------------------------------------+

+---------------------------------------------------------------------+
|          mantissa sign                               exponent sign  |
| pointer    |                                           |            |
| positions+---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|    ----> |13 |12 |11 |10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |  |
|          +---+---+---+---+---+---+---+---+---+---+---+---+---+---+  |
|          |   |                                       |           |  |
|          |   |                                       |           |  |
|          |   +------------- mantissa ----------------+- exponent +  |
|          |                                           |           |  |
|          +----------- mantissa and sign -------------+           |  |
|          |                                                       |  |
|          +----------------------  word --------------------------+  |
|                                                                     |
+---------------------------------------------------------------------+

+---------------------------------------------------------------------+
|Instructions                                                         |
+--------------+------------------------------------------------------+
|  A = 0       |                                                      |
|  B = 0       | Clears word-select portion.                          |
|  C = 0       |                                                      |
+--------------+------------------------------------------------------+
|  B = A       | Copies word-select portion                           |
|  C = B       |   from specified register                            |
|  A = C       |   to specified register.                             |
+--------------+------------------------------------------------------+
|  AB EX       | Exchanges word-select portion                        |
|  AC EX       |   between specified registers.                       |
|  CB EX       |                                                      |
+--------------+------------------------------------------------------+
|  A = A + B   |                                                      |
|  A = A + C   |                                                      |
|  C = A + C   |                                                      |
|  C = C + C   |                                                      |
|  A = A - B   |                                                      |
|  C = A - C   |                                                      |
|  A = A - C   | Performs stated arithmetic                           |
|  A = A + 1   |   on word-select portion.                            |
|  C = C + 1   |                                                      |
|  A = A - 1   |                                                      |
|  C = C - 1   |                                                      |
|  C = -C      |                                                      |
|  C = -C - 1  |                                                      |
+--------------+------------------------------------------------------+
|  A SR        |                                                      |
|  B SR        | Shifts word-select portion right.                    |
|  C SR        |                                                      |
+--------------+------------------------------------------------------+
|              |                                                      |
|  A SL        | Shifts word-select portion left.                     |
|              |                                                      |
+--------------+------------------------------------------------------+
|              | Circular shifts whole A                              |
|  A SLC       |   register but does not have                         |
|              |   word-select option.                                |
+--------------+------------------------------------------------------+
|  ? B = 0     |                                                      |
|  ? C = 0     |                                                      |
|  ? A => C    | Tests word-select portion of                         |
|  ? A => B    |   given register.                                    |
|  ? A = 0     |                                                      |
|  ? C = 0     |                                                      |
+--------------+------------------------------------------------------+
| Field-Select Options                                                |
|                                                                     |
|  1. Mantissa (M)                                                    |
|  2. Mantissa and Sign (MS)                                          |
|  3. Exponent (X)                                                    |
|  4. Exponent Sign (XS)                                              |
|  5. Sign of Mantissa (S)                                            |
|  6. Pointer (P)                                                     |
|  7. Word (W)                                                        |
|  8. Word thru Pointer (WP)                                          |
|                                                                     |
+---------------------------------------------------------------------+
|  Figure 2. Registers are 14 digits long with each digit being four  |
|  bits. An additional four bit register is used as a pointer. The    |
|  programmer can set the pointer to any digit position, change that  |
|  digit or all digits up to that position.                           |
+---------------------------------------------------------------------+

Some of the major routines such as those for sine, cosine, and tangent are the same from calculator to calculator. But in most cases if the code cannot be borrowed exactly as it exists in another calculator, it must be rewritten.

Some designer begin by strictly flowcharting the entire program Others tackle the code directly and leave all but basic flowcharting till the end for documentation purposes only. The code is written originally on paper just as you would write a program on an HP programming pad. It is then either punched on cards or typed into a handy CRT.

The major task in writing the microcode is not only to have the functions produce the correct answers when a key is pressed, but to fit the code into a given amount of memory and make it execute as fast as possible. Compacting the code, that is, rewriting sections of the program to make them more space-efficient, is easy enough, but sometimes results in a loss of speed. These are tradeoffs to which the designer must be constantly attentive.

The processor executes approximately three instructions per millisecond, with each instruction taking the same amount of time. The designer takes into consideration the type of function and the necessary speed when writing the code. Straight-line code with no branches of any I kind executes the fastest. For the label search function on the HP-67 and the HP-97 the designer duplicated a great deal of code to; make it faster. The print instructions for the new HP-19C, on the other hand, did not need to be as fast to keep up with the printer, mechanism. So the designer compacted these codes, making them very complex.

+---------------------------------------------------------------------+
|     +---------------+    +---------------+    +---------------+     |
|     |   A. Answer   |    |B. Multiplicand|    | C. Multiplier |     |
|     +---------------+    +---------------+    +---------------+     |
|                                                                     |
+--------+-----------+--------+---------------------------------------+
| LABEL  | CODE      |        | Explanation                           |
+--------+-----------+--------+---------------------------------------+
|        | A = 0     | W      | Clearing space for answer.            |
|        | P =       | 3      | Starting at least significant digit.  |
|        | GoTo      | Mpy90  | Starting in middle of loop for speed. |
| Mpy90  | A = A + B | W      | Add Multiplicand to partial product   |
|        |           |        |   the number of times specified by    |
|        |           |        |   digit being worked on.              |
+--------+-----------+--------+---------------------------------------+
| Mpy100 | C = C - 1 | P      |                                       |
|        | GoNC      | Mpy90  | NC stands for no carry, i.e. a GoTo   |
|        |           |        |   is executed unless a digit is       |
|        |           |        |   carried (or borrowed).              |
|        | ? P =     | 12     | Have we reached the end of the world? |
|        | GoYes     | END    |                                       |
|        |           |        |                                       |
+--------+-----------+--------+---------------------------------------+
|        | P = P + 1 |        | Move on the next digit.               |
|        | A SP      | W      | This does a divide by 10 to line up   |
|        |           |        |   for the next decade.                |
|        | GoTo      | Mpy100 | Go reenter loop.                      |
|        |           |        |                                       |
+--------+-----------+--------+---------------------------------------+
|  Figure 3. Multiplying two numbers uses the basic routine shown     |
|  above and involves three registers The starting point of this      |
|  code assumes the sign and exponent of the answer have already      |
|  been calculated. END is a common function return which would       |
|  perform operations such as display formatting, printing, etc.      |
+---------------------------------------------------------------------+

In general, programmable calculators go through more gyrations for each function than do preprogrammed calculators because they must generate an intermediate keycode. Where simple functions such as Change Sign, x exchange y, and ENTER require only 100 steps of code on a preprogrammed calculator, the same functions on a programmable calculator might take 150 steps. And a complex function such as rectangular-to-polar conversion might take over 4000 steps, depending on the argument keyed in.

The engineer uses a computer simulator to write and debug his code. Special programs written for this simulator furnish him with status bit information, register contents, and intermediate answers as an aid in this process.

Once the microcode is completed on the computer, it is transferred to an E-ROM (erasable read only-memory) simulator for further debugging (See photo.). The simulator is ideal for this because it is portable and easily updated as bugs are found and corrected. Simulated calculators are given to application engineers and quality assurance engineers to help locate problems.

After much editing, the microcode is ready to be converted into hardware. This usually takes several weeks. In the meantime, the simulators continue to be used heavily and, in most cases, additional bugs are found.

When the completed integrated circuit chips return, the first working models of the calculator are constructed. Final testing is then initiated. Some problems can only be discovered at this stage because of the peculiarities of simulated operation. For example, this is the first time low battery indicators can be checked since the E-ROM simulator does not work on batteries.

At long last, the revised code is ready to be sent for final chips. Although no problems are anticipated at this stage, testing continues to assure traditional Hewlett-Packard reliability.

The tremendous emphasis on testing of the calculators is for practical reasons as well incorrect programs cannot be easily corrected as they can be on large computers. Once the code is set in hardware, changes are costly and inconvenient.

When the final chips are approved for production, the development cycle is complete. The design engineer has spent anywhere from six months to 13 months perfecting his building block design. And whether the end product is a high-powered financial calculator like the HP-92 or a versatile keystroke programmable like the HP-19C, it is first an expression of his personality and creativity.


The Calculator Reference by Rick Furr (rfurr@vcalc.net)
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