Chapter Ten: It All Adds Up

Just as programs are written one statement at a time, knowledge of programming grows command by command. Each time you learn a new statement, you can instantly change the way you write programs. You may even go back and change your earlier programs, taking advantage of the power of newly learned statements to either simplify a program or to add new functions.

Although learning the language of BASIC is important, it is equally important to pay attention to how programs are put together. Programming has two parts: the statements, and the technique or logic. Technique is the know how of programming. Good technique means that a program is well writ- ten: the structure is clear, the routines make sense, program flow is easy to see, and variables have descriptive names. A poorly written program is bad news even when it uses fancy BASIC commands.

Good technique results from clear thinking and good planning. In chapter three, your BASIC vocabulary consisted of only six words: PRINT, CLS, INPUT, GOTO, IF-THEN, and END. Yet, even these six statements can be used to write useful, user friendly programs. What counts is not which statements are used but how they are arranged.

In this chapter, we will write a program that creates three-digit addition problems for you to answer. The program will keep track of your score. Nearly all of the commands used in this program have already been introduced. Now we will concentrate on program organization. Let's jump right in. Here is the mainline routine:

10  REM *********************************************************
20  REM *  PLUS1                                                *
30  REM *  Math drill: make up three-digit addition problems.   *
40  REM *********************************************************
50  CLS
60  NUMWRONG% = 0           'SET NUMBER WRONG TO ZERO
70  GOSUB 330               'DISPLAY INSTRUCTIONS
80  FOR NUMPROB% = 0 TO 9
90    RANDOMIZE TIMER
100   A% = INT(100 + RND * 899)
110   B% = INT(100 + RND * 899)
120   SUM% = A% + B%
130   PRINT
140   PRINT
150   PRINT " "A%
160   PRINT "+"B%
170   PRINT "_______"
180   INPUT ANSWER%
190 IF ANSWER% = SUM% THEN NEXT NUMPROB% ELSE GOSUB 410:GOTO 180
200 GOSUB 230               'DO THE SCORING
210 GOSUB 270               'DISPLAY THE SCORE
220 END

The program uses four subroutines. These are called by GOSUB statements on lines 70, 190, 200, and 210. Except for the GOSUB on line 190, each has a comment to the right explaining the job of the subroutine.

Line 60 assigns a value of zero to an integer variable called NUMWRONG%. The program uses this variable to keep track of the number of wrong answers. This line also has a comment to the right. It is a good idea to add comments to every line that creates a variable.

Line 80 begins a FOR-NEXT loop. Where is the end of the loop? The NEXT statement is part of the IF-THEN command on line 190. We will explain line 190 in great detail shortly. As the FOR-NEXT loop begins, the variable NUMPROB% is set to zero. NUMPROB% stands for number of problems. A loop of zero through nine displays ten addition problems.

The three digit numbers used in the addition problem are created by the next three lines. Line 90 seeds the random number generator with the number in TIMER. As you recall, TIMER holds the number of seconds, and hundredths of a second, since midnight. With the generator seeded, the RND function can be used in the next two lines to supply random numbers. The two random number formulas on lines 100 and 110 are a bit different than those we studied in chapter five. Let's explore what happens. We know that RND delivers a number in the range of .0000001 through .9999999. Look how RND is used in the formula. My Dear Aunt Sally tells us to do the multiplication first. So multiply .0000001 by 899. This gives us .0000899. Then add 100 to produce 100.0000899. The INT function does not round, so drop everything to the right of the decimal point. The final result is 100. The number 100 is the lowest possible random number which can be produced by our formula. Now try the other extreme. Multiply .9999999 by 899 to produce 898.9999. Add 100 to get 998.9999. Let INT drop everything to the right of the decimal point. 998 is the highest number which can be produced by our formula.

To check our results, enter this little program:

10 PRINT INT(100 + .0000001 * 899)
20 PRINT INT(100 + .9999999 * 899)

This random number formula produces numbers in the range 100 through 998. Therefore, we know that the program will always have two numbers, each of three digits, to display on the screen. One random number is assigned to the variable A% and another is assigned to B%.

Line 120 finds the answer to the addition problem. It is stored in an integer variable called SUM% and will be used to see if you have guessed correctly. Notice that SUM% is never PRINTed. Lines 130 through 170 display the problem. The first two PRINT statements just provide some blank space on the screen. Otherwise, the disply would be too cluttered. Then, line 150 PRINTs one blank space followed by the integer variable A%. The next line displays a plus sign (+) followed by B%. Since the plus sign takes up the space of one character on the screen, the blank space in the PRINT on line 150 is needed so the two numbers line up correctly. Finally, line 170 draws a line under the addition problem. The next move is up to you.

An INPUT statement on line 180 accepts the answer from the player. Their guess is stored in an integer variable called ANSWER%. Now we arrive at a complicated IF-THEN statement.

Line 190 closes the FOR-NEXT loop only if the human player answers correctly. Alternative one of the IF-THEN-ELSE statement is NEXT NUMPROB%. When a correct answer is given, the NEXT is executed and another trip through the loop begins: NUMPROB% is increased by one. If NUMPROB% is not greater than nine, then another two random numbers are generated nd displayed on the screen. On the other hand, if the human player answers incorrectly, then the ELSE part of the IF-THEN statement is executed. First, the GOSUB 410 branches to a subroutine which simply keeps track of the number of wrong answers. In this routine, which we will study later, NUMWRONG% is increased by one. Then a short message is printed, telling the player to try again. At the end of the subroutine, execution return back to the middle of the IF-THEN statement. The colon (:) adds another command which is part of the ELSE: GOTO 180. This branches back to the INPUT command so the player can enter another answer.

The FOR-NEXT loop can only start over when a correct answer is given to the addition problem. The NEXT NUMPROB% statement is only executed when ANSWER% is equal to SUM%. No matter how many tries it takes, the player must finally get the right answer before the program will move on and present another addition problem. And each wrong answer is counted by the subroutine at line 410.

Since the FOR-NEXT loop runs from zero to nine, a total of ten addition problems are created. All must be answered correctly before execution continues with line 200. BASIC does not stop the FOR-NEXT loop until NUMPROB% is greater than 9. NUMPROB% will be equal to ten by the time line 200 is executed. Therefore, NUMPROB% tells us how many addition problems we solved. This will be important when a score is calculated.

Two GOSUBs and an END statement wrap up the program. The first GOSUB calculates the score. The second displays the results. Now let us look at the subroutines.

SUBROUTINES

The first subroutine to be executed displays the instructions and performs one small trick.

330 REM *****  DISPLAY INSTRUCTIONS  *****
340 PRINT "**********************************************************"
350 PRINT "*  You will be given ten addition problems.  I will keep *"
360 PRINT "*  track of your score.                                  *"
370 PRINT "*  Press ENTER when you are ready to begin.              *"
380 PRINT "**********************************************************"
390 INPUT GARBAGE$
400 RETURN

Notice line 390. The program stops after displaying the directions. The INPUT on line 390 waits for input from the keyboard. The reply, which should be nothing more than pressing the enter key, is stored in a string variable named GARBAGE$. This name is really descriptive. It is called GARBAGE$ because its contents are thrown away. Nothing is ever done with GARBAGE$. This variable is a garbage can instead of a mailbox. Its only purpose is to stop the program until the person using the computer reads the directions and is ready to begin.

The next subroutine is called whenever someone enters a wrong answer:

410 REM *****  WRONG ANSWER  *****
420 NUMWRONG% = NUMWRONG% + 1
430 PRINT "Try Again"
440 RETURN

This is the subroutine which is called from inside of the ELSE portion of the IF-THEN-ELSE statement on line 190. NUMWRONG%, which had been set to zero on line 60 at the beginning of the program, is increased by one. A short message is displayed on the screen, and then execution returns for the rest of line 190.

Once ten addition problems have been answered it is time to calculate a score. This is an interesting algorithm.

230 REM *****  DO THE SCORING  *****
240 HUNDREDTHS! = NUMPROB% / (NUMPROB% + NUMWRONG%)
250 PERCENT% = HUNDREDTHS! * 100
260 RETURN

Our FOR-NEXT loop demands that you keep trying a problem until you get it right. This is different from most tests. Usually you get one try at a problem and if you are wrong, the question is marked incorrect and you lose points. In this program, you also lose points, but you have to try again on the problem. Because of this, each answer counts as a separate problem. Therefore, the total number of problems is equal to the ten which must be answered correctly to complete the FOR-NEXT loop plus the number of wrong answers. This is not your ordinary test.

Check out line 240. Now we can see why NUMPROB% runs a FOR-NEXT loop from zero to nine. The loop does not stop until NUMPROB% is equal to ten. Ten is the number of addition problems which were answered correctly. It is no accident that the loop uses zero through nine. This program can display any number of addition problems. Only the upper limit on the FOR-NEXT loop needs to be changed! The scoring subroutine knows, by looking at NUMPROB%, how many problems were answered correctly. This is good planning.

Line 240 produces a score in hundredths. It is stored in a single precision variable. To convert from hundredths into a more familiar percentage value, line 250 multiplies HUNDREDTHS! by 100. This is the overall score.

This scoring subroutine is not the only one possible. For example, if only ten addition problems are created, then each wrong answer could count ten points. Multiply the number of wrong answers by ten and subtract that sum from 100 percent to find the score. This plan has a problem if someone takes more than ten incorrect guesses to complete the test. They would end up with a score below zero! Since scoring happens in a subroutine, you might wish to try out this or another algorithm.

RACE AGAINST THE CLOCK

Scoring 100 percent on addition problems is easy if you have plenty of time. To make the test a little tougher, let us see how quickly a person can solve the ten problems. Add these lines and then LIST the entire program to see how the structure is changed.

20  REM *  PLUS2                                                *
75  BEGTIME! = TIMER        'STORE BEGINNING TIME
195 ENDTIME! = TIMER        'STORE ENDING TIME
205 GOSUB 450               'CALCULATE THE TIME
305 PRINT "Your time was"MINUTES%"minutes,"SEC%"seconds."
365 PRINT "*  You will be timed.                               *"
450 REM ***** CALCULATE THE TIME  *****
460 ELAPSED% = ENDTIME! - BEGTIME!
470 SEC% = ELAPSED% MOD 60
480 ELAPSED% = ELAPSED% - SEC%
490 MINUTES% = ELAPSED% \ 60
500 RETURN

First, notice that we are using the TIMER function again. This time we are using it not merely to have some strange numbers to seed the random number generator. We are using it as a real stopwatch timer. Line 75 stores TIMER in a single precision variable called BEGTIME!. The position of this statement is important. Recall that the display instructions subroutine beginning on line 330 asks the player to Press ENTER when you are ready to begin. As soon a someone presses the enter key, line 75 is executed and the value in TIMER is stored in the BEGTIME! variable. At that moment, the clock starts ticking.

After all problems in the FOR-NEXT loop have been answered correctly, BASIC continues execution of the program. The first instruction after the loop is line 195. This stores TIMER in another single precision variable called ENDTIME!. Using BEGTIME! and ENDTIME! we can count the number of seconds used to solve the ten addition problems. To do this calculation, line 205 adds a GOSUB to run the subroutine beginning at line 450.

The input to the subroutine consists of the two time variables, BEGTIME! and ENDTIME!. The output will be another two variables, one with the number of minutes and another with the number of seconds. Four statements are needed to turn the input into output.

Since TIMER holds the number of seconds since midnight we must do some subtraction to find out the number of seconds which have elapsed while the program was running. Line 460 subtracts BEGTIME! from ENDTIME! and stores the difference in an integer variable called ELAPSED%. Putting the elapsed time into an integer variable causes BASIC to round any fractional seconds, like hundredths, into a whole number. ELAPSED% is the number of seconds used to solve the ten addition problems.

The number in ELAPSED% certainly tells us how long a person took to answer the questions, but this time is in seconds. We need to convert this number into ordinary minutes and seconds, like 2:30 to show two minutes, thirty seconds. To do this, the subroutine uses a new BASIC operator. When we divide ELAPSED% by 60 the result is the number of whole minutes plus a remainder in seconds. If we used ordinary division, dividing 150 seconds by 60 would result in 2.5. While 2.5 minutes is, indeed, the same as 2:30, it does not yet look like an ordinary time. What we need is a way to find the remainder when dividing 150 by 60. The MOD operator provides this ability.

Look at line 470. Suppose ELAPSED% held the number 150. The statement:

470 SEC% = ELAPSED% MOD 60

makes SEC% equal to the remainder which is left after 150 is divided by 60. MOD does not tell us how many times 60 went into 150. It simple stores the remainder. For example, these three statement all produce the same number:

10 PRINT  90 MOD 60
20 PRINT 150 MOD 60
30 PRINT 210 MOD 60

MOD is an operator just like add (+), subtract (-), and multiply (*). It means give me the remainder. MOD is not an operator that you will use often. However, it is handy when calculating times.

Now that we have the number of seconds safely stored in the integer variable SEC%, we need to find the number of minutes. First, let's remove these extra seconds from ELAPSED%. Line 480 subtracts SEC% from ELAPSED%. Finally, line 490 divides ELAPSED% by 60 to produce the number of minutes. We know that the division will produce a whole number because line 480 subtracted out the remainder. To check our work, multiply the number of minutes by sixty, add the number contained in SEC%, and make sure this matches the number of seconds held in ELAPSED%.

The two variables MINUTES% and SEC% are used as part of the output display at the end of the program. Line 305 is added to PRINT the time following the score.

CHALLENGES

Once you have become a wizard at adding three digit numbers in your head, try using PLUS2 as a model for creating other arithmetic programs. Here are some ideas:

SUBTRACTION

• A subtraction program could be easily created by making slight changes.
• To avoid having a negative number as an answer, change line 110 to a random number formula that produces only two digit numbers. Refer to "Random Number Formulas" on page 56 to review.
• Change line 120 from addition to subtraction. Also, change the name of the variable from SUM% to DIFFERENCE%.
• The plus sign (+) on line 160 must be changed and an extra space should be added so that the two numbers in the subtraction problem line up correctly.
• Finally, change the directions on line 350.

MULTIPLICATION

Multiplication of two three-digit numbers in your head without using scratch paper might be a little tough.

• Change both random number formulas on lines 100 and 110. Perhaps A% should be a one or two digit number and B% should only be a single digit. Again, refer to "Random Number Formulas" on page 56 for help with new formulas.
• Change SUM% to PRODUCT% everywhere it is used.
• Change the addition symbol to an asterisk (*).
• Enter new directions.

DIVISION

A division program is more difficult. Two solutions are possible. The first solution could demand the player enter a quotient and a remainder:

• Change the random number formulas so that a two digit number is divided by a one digit number.
• Use the MOD operator to find the remainder.
• Use integer division to find the quotient.
• Change the statements around line 180 to ask for both parts of the answer.
• Construct IF-THEN statements to check if both the quotient and the remainder are correct.
• Change the directions.

Another solution avoids the problem with remainders.

• Change the random number formulas so they both produce single digit numbers (greater than zero).
• Multiply these together.
• Use the product and one of the random numbers as a division problem to display on the screen. The answer, of course, is the other random number. Here is an example:

Let A% equal 4.

Let B% equal 6.

Multiply the two and store the result in PRODUCT%.

Display the problem:

PRINT PRODUCT% "divided by"A%"="

which would appear as:

24 divided by 4 =

INPUT ANSWER% and check to see if it is equal to B%.

MENU

Once programs for addition, subtraction, multiplication, and division are ready, write a menu program to RUN each of these others. Replace the END statement on line 220 to return control back to the menu.