## Monday, January 16, 2017

### Fun with the Sharp EL-5500 III

Fun with the Sharp EL-5500 III

Even though the EL-5500 III has one programming space, we can fit many programs in it.  One of the great features is that how programs take relatively little space.  Obviously you can change the line numbers, the sequence of lines are most important.

Euclid Algorithm – RUN 10

10 PAUSE “GCD: A>B”
18 INPUT “A: “; A, “B: “; B
20 C = A – INT(A/B)*B
30 IF C = 0 THEN 40
32 A = B
34 B = C
36 GOTO 20
40 PRINT “GCD = “; B
46 END

My first program on the EL-5500 III.  We can probably make the coding more efficient.  PRINT with a proceeding WAIT pauses execution until [ ENTER ] is pressed.

The command END ends the program execution and allows the space to have more than one routines.

Examples:
A: 100, B: 20.  Result:  GCD = 20
A: 63, B: 60.  Result:  GCD = 3

Binomial Expansion – RUN 50

50 PAUSE “(Ax + B)^n”
55 INPUT “A: “;A, “B: “;B, “N: “,N
60 FOR I=0 TO N
65 C = FACT(N) / (FACT(I) * FACT(N-I))
70 T = C * A^(N-I) * B^I
75 PRINT T; “*x^”; N-I
80 NEXT I
85 END

The command PAUSE shows the text for about 0.85 seconds.

This program displays each coefficient one at time.

Example:  A = 3, B = -2, N = 3.  Expand (3 – 2x)^3.
Result:  27, -54, 36, -8  (27x^3 – 54x^2 + 36x – 8)

Days Between Dates – RUN 100

100 PAUSE “Days between Dates”
112 INPUT “M1:”; M1, “D1:”; D1, “Y1:”; Y1
113 INPUT “M2:”; M2, “D2:”; D2, “Y2:”; Y2
115 M = M1: D = D1: Y = Y1
117 GOSUB 140
119 F1 = F
121 M = M2: D = D2: Y = Y2
123 GOSUB 140
125 F2 = F
127 N = F2 – F1
129 PRINT “# DAYS: “; N
131 END
140 IF M > 2 THEN 150
142 X = 0: Z = Y – 1
144 GOTO 160
150 X = INT(.4 * M + 2.3): Z = Y
160 F = 365 * Y + 31* (M – 1) + D + INT(Z/4) – X
165 RETURN

If I had it my way, every calculator that isn’t a basic 4-function calculator will have a Days Between Dates function.

Example:  November 4, 1986 to January 12, 2017
M1:  11, D1: 4, Y1: 1986
M2: 1, D2: 12, Y2: 2017
Result:  11,027

Power of a Complex Number – RUN 200

This calculates (a + bi)^n

200 PAUSE “(A + Bi)^n”
203 INPUT “A: “;A, “B: “;B, “n: “;N
205 IF A<>0 THEN 210
207 A = A^N: GOTO 220
210 R = √(A^2 + B^2)^N
212 T = ATN(B/A)*N
214 A = R * COS T
216 B = R * SIN T
220 PRINT A; “+”; B; “i”
225 END

The command <> means not equals (≠) and ATN is the arctangent function.

Examples:
(2 + 3i)^3:  A = 2, Bi = 3.  Result: -46 + 9i
(-5 + i)^2:  A = -5, Bi = 1.  Result: 24 – 10i

Error Function Approximation – RUN 250

250 PAUSE “APPROX ERF(X)”
252 CLEAR
254 DIM A(3)
256 E = 0
260 INPUT “X > 0 : “; X
262 T = RCP(1 + .47047 * X)
270 FOR I = 1 TO 3
274 E = E + A(I) * T^I
276 NEXT I
280 DATA .3480242, -.0958798, .7478556
290 E = 1 – E * EXP(-(X^2))
292 PRINT “ERF : “, F
294 CLEAR
296 END

Use the command CLEAR to clear all the variables.  At this point, I will use this command both at the beginning and end of calculations.  The command RCP is the reciprocal.  Finally, EXP is from e^x function, not the [EXP] key.

Example:
x = 0.53, erf ≈ 0.546455764
x = 0.88, erf ≈ 7.86708E-01 = 0.786708

Keep in mind this approximation is accurate 2.5 parts in 10^-5.

Source:  Smith, Jon M.  Scientific Analysis on the Pocket Calculator  John Wiley & Sons: New York. 1975.  ISBN 0-471-79997-1

Simpson’s Rule – RUN 300

Calculates the numeric integral ∫ f(x) dx from x = L to x = U.

You can edit the function at line 342.  In BASIC-PRO mode, call up line 342 by LIST 342.  Edit as desired.

300 PAUSE “Simpsons Rule”
302 CLEAR
304 INPUT “LOWER: “; L, “UPPER: “; U, “PARTS (even): “; N
308 X = L: GOSUB 340: T = F
310 X = U: GOSUB 340: T = T + F
314 H = (U – L)/N
320 FOR I = 1 TO N-1
322 X = L + I * H: GOSUB 340
324 R = I/2 – INT(I/2)
326 IF R = 0 THEN LET T = T + 2*F
328 IF R <> 0 THEN LET T = T + 4*F
330 NEXT I
332 T = T * H/3
334 PRINT “Integral: “, T
336 CLEAR
338 END
340 REM f(x)
342 F = [insert f(X) here]
344 RETURN

Note:  I finally learn why LET is included in BASIC.  In an IF-THEN statement, if you want to assign a value or calculation to a variable, you will need a LET command.

I use a REM (remark) command on line 340.  REM is for comments and nothing said after REM is executed.

Examples:

342 F = X^2 – 1
L = -2, U = 2, N = 14.  Result:  1.333333334 (Actual: 4/3 ≈ 1.333333333)

342 F = √(X – 1)
L = 2, U = 3, N = 14.  Result: 1.218951372 (Actual:  ≈ 1.2158951416)

Dancing Star Demo – RUN 400

400 PAUSE “Dancing Star Demo”
405 CLEAR
410 S\$ = “         “  (9 spaces)
415 FOR I = 1 TO 48
420 N = RND 7 + 1
425 T\$ = MID\$(S\$, 1, N-1) + “*” + MID\$(S\$, N+1, 9-(N+1))
430 WAIT 15: PRINT T\$
440 NEXT I
445 BEEP 3: CLEAR: END

This is just show a dancing asterisk (*) on the screen.

WAIT 15: PRINT T\$:   This causes the string T\$ after a quarter of a second.  WAIT operates in 1/60 seconds.

RND n:  This is the random command.  If n = 1, the result is between 0 and 1.

BEEP n:  This makes the EL-5500 III beep n times.

Eddie

This blog is property of Edward Shore, 2017.