├OMPUTERS CALCULATE AT LIGHTENING SPEED. ┼VERYBODY KNOWS THAT. ╠ET'S SEE IT HAPPEN WHILE WE ALSO TAKE A LOOK AT SOME INTERESTING SETS OF NUMBERS.
Ç*CN1;--- ╞╒╬ ╬╒═┬┼╥╙ ---Ç*CN0
╘YPE WHAT YOU SEE BELOW AND PRESS ╥┼╘╒╥╬ TO GET THE ANSWERS:
Ç*FP3
╨╥╔╬╘ 3367 * 297
╨╥╔╬╘ 3367 * 165 , 3367 * 99
╨╥╔╬╘ 3367 * 15 ; 3376 * 25 ; 3367 * 35
╘HE ASTERISK IS USED TO MULTIPLY NUMBERS. ├AN YOU SEE A PATTERN IN THIS BUNCH OF RESULTS? ╫HAT DO YOU THINK IS THE RULE? ├OULD YOU TRY WRITING A LITTLE PROGRAM USING THE RULE YOU JUST DISCOVERED? ╔NCIDENTALLY, DON'T FORGET TO NOTICE THE RULE OF PRINTING: WHAT DO THE SEMICOLON AND THE COMMA DO?
╚ERE IS ANOTHER NUMBER THAT OPENS UP DOORS TO ALL SORTS OF FUN.
╨╥╔╬╘ 98765432 / 8
╚MMM... ╫HAT DO YOU THINK? ╬OTE THE MISSING 8 IN THE RESULT OF THIS DIVISION. ╘HE RESULT ALSO IS A FUN NUMBER TO PLAY WITH. ╘RY THESE:
╨╥╔╬╘ 12345679 * 36, 12345679 * 45, 12345679 * 63
╘HAT LAST BATCH OF NUMBERS USED TO BE CALLED UPON, LONG AGO, IN THE AGE OF MECHANICAL CALCULATORS. ╘HE REPAIRMEN DIDN'T HAVE TO DO ANY HAND CALCULATIONS TO CHECK THE MACHINES. ╘HEY JUST USED THE FUN-NUMBERS TO CHECK THEIR FIXING. ╘HEY KNEW RIGHT AWAY IF THEY FIXED THINGS RIGHT. ├AN YOU SEE WHY?
*** ╨╥╧╩┼├╘╙ ***
╫HAT MAKES THOSE NUMBERS BEHAVE AS THEY DO? ╫HAT ARE THE RULES OF THE PATTERN? ┘OU DON'T HAVE TO KNOW MUCH MATH BEYOND ARITHMETIC TO PLAY WITH NUMBERS, AND LEARNING TO SEE PATTERNS IS QUITE HANDY IN LEARNING TO PROGRAM A COMPUTER.
╔F YOU LIKE PLAYING WITH NUMBERS AND RELATE THEM TO COMPUTER WORK, ═ARTIN ╟ARDNENER'S ═┴╘╚┼═┴╘╔├┴╠ ╟┴═┼╙ COLUMN IN THE ╙├╔┼╬╘╔╞╔├ ┴═┼╥╔├┴╬ IS A GOOD PLACE TO LOOK FOR IDEAS, SUGGESTIONS AND CODING ALGORITHMS.
Ç*CN1;--- ╨╠┴╔╬ ╬╒═┬┼╥╙ ---Ç*CN0
╬UMBERS CAN BE PRINTED BY A COMPUTER FROM THE STRANGEST LOOKING EXPRESSIONS, ALL OF WHICH COME HANDY IN PROGRAMMING. ╠OOK AT THESE EXAMPLES:
Ç*FP2
╨╥╔╬╘ ╙╘╥$(5);╙╘╥$(-5);╓┴╠("123");
╓=-2.5:╨╥╔╬╘ ╓;-╓;╙╘╥$(╓);╙╘╥$(-╓)
╓= 2.5:╨╥╔╬╘ ═╔─$(╙╘╥$(╓),2)
╘HE ╙╘╥$(NUMBER) COONVERTS A NUMBER INTO A CHARACTER STRING, ╓┴╠("STRING") DOES THE OPPOSITE. ┴ND ═╔─$, OF COURSE, IS OUR FAMILIAR STRING-PIECE-TAKER, IN THIS CASE IT WORKS IN A ROUNDABOUT WAY TO TAKE THE DIGITS BEGINNING WITH THE SECOND ONE.
*** ╨╥╧╩┼├╘ **
╔N THE LAST EXAMPLE SUBSTITUTE A NEGATIVE VALUE, SUCH AS -2.5 TO SEE WHAT COMES OUT.
╘O TRY YOUR HAND AT SOME CALCULATIONS, WRITE A LITTLE PROGRAM TO HANDLE NUMBERS 1 TO 5 AS FOLLOWS: CHANGE 1 TO 5, 2 TO 4 ... AND SO ON, UNTIL 5 TO 1. ╨RINT THEM A PAIR ON A LINE, LIKE THIS:
Ç*FP5
1 5
2 4
3 3
4 2
5 1
╘HEN USE A DIFFERENT BUNCH OF NUMBERS, PERHAPS A WIDER RANGE, PERHAPS NUMBERS NOT STARTING AT 1. ┼NJOY THE CHALLENGE!
Ç*CN1;--- ╬╒═┬┼╥ ╟╒┼╙╙╔╬╟ ---Ç*CN0
┴S A MILD ENTERTAINMENT, HERE IS A SIMPLE NUMBER GUESSING GAME. ╬OTHING PROFOUND, BUT IT SHOWS LOOPS, RANDOM NUMBER SETUP AND DECISIONS BEING MADE BY THE COMPUTER, AND THE COMPUTER'S COMMUNICATION WITH THE PERSON PLAYING THE GAME:
// PRG: THINKNUMBER //
Ç*FP7
*** ╓┴╥╔┴┬╠┼╙ ***
╬1 AND ╬2 ARE LOWER AND UPPER LIMITS OF
THE NUMBER TO GUESS
╬% NUMBER THE COMPUTER IS THINKING OF
╬$ WHAT YOU GUESS (IN STRING FORM)
╓% SAME THING IN NUMBER FORM
*** ╔╬╙╘╥╒├╘╔╧╬╙ ***
╥╒╬ THE PROGRAM AND FOLLOW THE SCREEN PROMPTS UNTIL YOU GET THE CORRECT ANSWER. ╘O QUIT ENTER"╤" INSTEAD OF A NUMBER.
*** ─┼╘┴╔╠╙ ***
┴ WHOLE RANDOM NUMBER IS DEVELOPED BY THE COMPUTER IN LINE 150. ╔T CAN RANGE FROM ╬1 TO ╬2. ┘OU GET A CHANCE TO GUESS IT SEVERAL TIMES. ╘HE COMPUTER CHECKS IF YOUR GUESS MATCHES THE TARGET NUMBER.
╘HE DECISIONS ARE SIMPLE. ╔F THE NUMBER YOU GUESSED IS NOT RIGHT, THE COMPUTER PRINTS A MESSAGE TO THAT EFFECT AND GOES BACK FOR MORE TRIES TO LINE 180. ╫HEN YOU ARRIVE AT THE RIGHT GUESS, YOU'RE TOLD ABOUT IT IN LINE 240. ╘HEN A NEW GAME CAN BEGIN WITH A NEW NUMBER. ╚ERE IS A TYPICAL OUTPUT OF SOME GUESSING:
// PIC: THINKNUMB //
*** ╨╥╧╩┼├╘╙ ***
├HANGE THE RANGE OF NUMBERS THE COMPUTER PICKS.
┘OU CAN READ IN THE MANUAL ABOUT ┬ASIC KEYWORDS: ╥╬─, ╔╬╨╒╘, ╓┴╠, ╔╞, ╘╚┼╬, ╨╥╔╬╘, AND ╟╧╘╧. ╥EADING ABOUT THE VARIOUS FORMS OF THE ─╧...╠╧╧╨ STATEMENT IS A GOOD IDEA.
╠EARN ABOUT VARIABLES WHICH HAVE A PERCENT TACKED ON TO THE NAME. ╔T MEANS AN INTEGER VALUE, A WHOLE NUMBER. ╔F ╓ IS 1.5 IT'S INTEGER VALUE IS 1. ╨ERCENT VARIABLES AREN'T USED OFTEN, BUT IT'S GOOD TO BE FAMILIAR WITH THEM. ┴ND JUST AS "$" IN CHARACTER STRINGS HAS NOTHING TO DO WITH MONEY, THE PERCENT SYMBOL, "%" HAS NOTHING TO DO WITH CALCULATING PERCENT. ╔F YOU ARE PUZZLED BY THESE STRANGE, MEANINGLESS, DESIGNATIONS, YOU ARE NOT ALONE.
Ç*CN1;--- ╚┴╠╞ ╘╔═┼ ─┼├┴┘ ╘╧╫┴╥─╙ ┌┼╥╧ ---Ç*CN0
╔F YOU HAVE ONE MILLION ATOMS OF URANIUM IN 1984, WHEN WILL ALL ITS RADIOACTIVITY DIE AWAY ASSUMING THAT HALF OF ITS ATOMS BECOME INERT IN A DAY? ╚OW ABOUT WASHING OUT THE FIXER IN A PHOTOGRAPHIC PROCESSING? ┴SSUME THAT EACH RINSE DILUTES THE SOLUTION IN HALF. ╔S THE SOLUTION EVER FREE OF FIXER? ╙IMILARLY, IF YOU BEGIN WALKING FROM THE EDGE OF THE CIRCLE TOWARDS ITS CENTER, AND WITH EACH STEP YOUR STEP SIZE IS DIVIDED IN HALF, WILL YOU EVER REACH THE CENTER OF THE CIRCLE? ╘HIS ROUTINE ILLUSTRATES HOW WE MIGHT GO ABOUT THE SOLUTION:
// PRG: HALF TIME //
Ç*FP9
*** ╓┴╥╔┴┬╠┼╙ ***
┌$ A LONG STRING OF ZEROS USED TO PRINT
LONG NUMBERS
╬ THE NUMBER YOU INPUT TO THE PROGRAM
╬$ THE SAME THING IN STRING FORMAT. ╔T IS
ALSO REUSED TO HOLD THE ANSWER
╪ FLAGS THE THREE SIZES OF NUMBERS (NORMAL,
UNDER ZERO OR HUGE)
*** ╔╬╙╘╥╒├╘╔╧╬╙ ***
╫HEN YOU ╥╒╬ THIS PROGRAM, ANSWER THE ╔╬╨╒╘ QUERY WITH ANY NUMBER AND WATCH THE COMPUTER GO THROUGH THE NECESSARY STEPS TO A SOLUTION. ╘O QUIT, JUST PRESS THE ╙╘╧╨ KEY DURING THE LONG PRINOUTS.
*** ─┼╘┴╔╠╙ ***
╔S THERE A SOLUTION ? ╘HE ANSWER IS NEVER, BUT THE PROCESS IS INTERESTING: WE HAVE TO REPAETEDLY DIVIDE A NUMBER BY TWO. ├AN WE REACH ZERO? ├AN WE HANDLE HUGE OR VERY TINY NUMBERS? ┘ES AND NO.
╘HIS PROGRAM TAKES A NUMBER, DIVIDES IT BY 2 AND PRINTS THE RESULT. ┘OU CAN SEE HOW LONG IT TAKES TO REACH ZERO. ┬Y DEFINITION - FOREVER. ╔N THIS SORT OF EXPERIMENT YOU CANNOT REACH ZERO.
// PIC: HALFTI //
╙OME NUMBERS IN THE COMPUTER ARE SO SMALL OR BIG, THAT THEY CAN'T BE SHOWN IN THEIR NORMAL FORMAT. ┴ "SCIENTIFIC" NOTATION IS USED FOR THEM. ┘OU CAN READ ABOUT IT IN THE MANUAL. ╚ERE IS A PROGRAM WHICH DECODES THE SCIENTIFIC NOTATION FROM A NUMBER SUCH AS 1.6┼-04 TO 16/10000. ╫E RARELY NEED TO DO THIS SORT OF DECODING, BUT THIS PARTICULAR APPLICATION IS INTERESTING.
╚OWEVER, THE COMPUTER ACTUALLY MANGLES THE RESULTS, BECAUSE WHEN THE NUMBER BECOMES TOO SMALL TO HANDLE (OVER 39 ZEROS!) IT STUFFS ITS OWN ZERO. ╔T SHOULD REPORT ╒╬─┼╥╞╠╧╫ ┼╥╥╧╥, BUT DOESN'T. ╔F THE COMPUTER WERE ABLE TO COUNT TO MORE DIGITS OF ACCURACY, A ZERO WOULD NEVER BE REACHED.
╩UST TO MAKE THIS ROUTINE COMPLETE IN THE OTHER DIRECTION, IF YOU REMOVE THE ╥┼═ARK FROM LINE 170 AND INSERT ONE IN LINE 180, YOU'LL SEE THE OPPOSITE PROCESS - MULTIPLYING BY 2, FOREVER. ╧NCE AGAIN, THE COMPUTER QUITS - IT CANNOT REACH INFINITY. ┬UT THIS TIME, IT HONESTLY ADMITS ITS PREDICAMENT BY REPORTING AN ╧╓┼╥╞╠╧╫ ┼╥╥╧╥.
╙CIENTIFIC NOTATION IS COMPACT AND USEFUL. ╨RINTING NUMEROUS ZEROS IS NORMALLY A NUISANCE, BUT ISN'T IT FUN WATCHING ALL THOSE ZEROS PRINT?
