Addition--Computer Problem Solving

PROGRAM ADD(INPUT, OUTPUT); {line 1}

This program statement is an introduction. It tells the computer "this is a program called ADD, and it will accept input from the user and produce output."

In the vocabulary of Pascal, it tells the computer quite specifically that information will come from the keyboard (INPUT, which happens to be the file $STDIN during a session). And it tells the computer that information will be returned to the video screen (OUTPUT, which happens to be $STDLIST during a session). Now the computer knows which of its parts (in addition to the processor) will be active.

A different introductory statement could be used to tell the computer that information will come from another source or go to another destination.

VAR DIGITS, TOTAL : REAL; {line 2}

This is another introductory statement. It tells the computer "create two variables (places to hold something in memory) and make them big enough to hold numbers with fractions." Numbers without fractions take up less room in memory than do numbers with fractions.

VAR means "variable." In the vocabulary of Pascal, it tells the computer that the words DIGITS and TOTAL will be used to hold something.

REAL tells the computer that what will be held in DIGITS and TOTAL will be numbers and, more precisely, that these numbers might include fractional parts (263.6, for instance).

For as long as the program is active, the computer understands that DIGITS and TOTAL really stand for numbers. Numbers without fractional parts are called integers.

This might seem unnecessary. Computers work with numbers, do they not? But this and every other statement is vital to the program. From this statement, the computer knows that whatever is put into the variables DIGITS and TOTAL must be numbers (and only numbers), not letters or words. It knows, too, that it must create in its electronic memory two distinct places to hold numbers.

BEGIN {line 3}

"Now, after all this introductory material, here is what you (the program) will do." This statement signals the end of the introductory material and the beginning of the main body of the instructions.

TOTAL := 0; {line 4}

"Begin with a sum of zero." The computer must be told explicitly where to start. Where it starts is by putting the value 0 (zero) into the area of memory represented by the variable TOTAL. Without this statement, there is no way to predict what the starting value of TOTAL might be, and that could cause problems. (As yet, the area of memory represented by the variable DIGITS holds no useful value.)

readln(DIGITS); {line 5}

"Take a number from the keyboard." Implicit in this statement is the instruction to "remember" the number that comes from the keyboard by putting it into the memory area called DIGITS.

while DIGITS <> 0 do {line 6}

"Examine the number taken from the keyboard. If it is not equal to zero, look for the begin following do and start there. If the number is zero, proceed to the step following the next end that you find." (The <> means "is not equal to" or "does not equal.")

There are a lot of instructions in this one, short statement. Programming languages are precise, and they compress a lot of meaning into very few words.

A very natural question at this point is, "Why not say 'if' if you mean 'if'?"

The answer lies in the meaning of the "words" used in the Pascal instructions. Pascal's while and if are called conditionals--they are decision-makers. In its simplest use, Pascal's if means "make this comparison, make a decision, then continue."

Pascal's while, on the other hand, means "for as long as some condition is true...." And that is what we want the program to do: we want to be able to enter many different numbers, over and over, and have them added, one after another, to yield a sum. And we want the computer to stop taking and adding numbers when we enter a zero.

In the language of Pascal, while is a convenient way to start a loop--a sequence of steps that is repeated, over and over, until we give the computer some reason to cease the repetition. Each time we enter a number, while says: "Is this zero? If it is not zero, do whatever comes after the next begin. If it is zero, look for the next end and pick up the instruction that follows."

begin {line 7}

"Start here and follow the next sequence of instructions until you find an end; statement." What follows are the instructions to be followed over and over (in a loop)--until zero is entered at the keyboard.

TOTAL := TOTAL + DIGITS; {line 8}

"Perform addition." Clearly this is not the addition that you were taught in school. It is, however, correct and precise in the "grammar" of Pascal.

More accurately, this instruction reads: "Take the value found in the memory area called TOTAL, add to it the value found in memory area called DIGITS, and insert the sum back into the memory area called TOTAL."

TOTAL no longer holds the value zero. Zero has been "erased." Instead it holds the new value found by adding the old value to whatever number that we entered at the keyboard.

readln(DIGITS); {line 9}

"Take another number from the keyboard and place it in the memory area called DIGITS." The new number that we entered takes the place of the number we entered previously.

end; {line 10}

"End of the loop." This is a form of punctuation. It concludes the steps begun in statements 6 and 7. And in this case, it sends the program running back to the while conditional. Because while signals repetition, the computer returns to the instruction in statement 6 and finds that it must perform another examination of the number entered.

If at any time we enter 0 (zero), the computer will discover that the condition defined in statement 6 (is not zero) has not been met. Until we enter zero, the computer will continue to take numbers, one number at a time, perform addition, juggle its memory, and wait for still another number.

Recall that this circular repetition of one or more steps is called a loop.

If we enter 0 (zero), the computer will break out of the loop dictated by while and proceed to the next (and in this instance, the last) step in the procedure.

writeln(TOTAL : 10 : 2); {line 11}

"Show the total that you computed." This last instruction tells the computer to display the sum of all of the additions that it has performed. More accurately, it displays the value that it finds in the memory area called TOTAL, and that value is the sum of the additions. A piece of the instruction, : 10 : 2, tells the computer how to display the number -- in this case, as a number occupying the space of ten characters on the screen, with two digits following the decimal point.

Displaying images on the video screen is also under the control of the system processing unit.

END. {line 12}

"The program is done." This is the last mark of punctuation. This tells the computer to stop the program.