Sunday, May 23, 2021

Sharp EL-5100 Programs

 Sharp EL-5100 Programs



We can use the formula programming engine of the classic Sharp EL-5100 (1979) to store multiple formulas and invoke some simple programs.

Quadratic Formula

ax^2 + bx + c = 0

x = (-b ± √(b^2 - 4ac)) / (2a)

Formulas (AER Mode):

1; f(A,B,C)=(B²-4AC) STO D ◣
2; (-B+√D)÷(2A STO E, (-B-√D)÷(2A STO F

Instructions (COMP Mode):

1.  Press [ 1; ], enter A, B, and C.   D is shown as ANS 1.  If D ≥ 0, then the polynomial have real roots.  Continue to the next step.  If D < 0, then the polynomial has complex roots, stop. 
2.  Press [ 2; ], the two roots are displayed.

Examples:

Example 1:  A = 1, B = -1, C = -3.75;  Results:  2.5, -1.5

Example 2:  A = 2, B = 26, C = 84; Results:  -6, -7


Power of a Complex Number (Principal)

(a + bi)^c  = d + ei   

The →POL stores θ in I and displays r, which r is not automatically stored.

Formulas (AER Mode):

1; f(A,B,C)=A →POL B STO I, I^C×COS(JC) STO D, I^C×SIN(JC) STO E

^ represents Y^X.  

Instructions (COMP Mode):

1.  Set the calculator to Radians mode.  Press [ 1; ]. 
2.  You get three results:  I  (r), real part, imaginary part.   Press [ COMP ] to see each result (ignore the first result)

Examples:

Example 1:  (4 + 4i)^3 = -128 + 128i;  r = 5.56854249

Example 2:  (5 - 6i)^0.5 = 2.5308348108 - 1.18537961766i;  r = 7.810249676

Confidence Interval

Here, we can use one formula to store values for use in the next formula.

confidence interval = A ± J * B / √C

where:
A = mean
B = variance
C = n
J = z*  (see table below)

z* values:
F:  99% confidence level, value = 2.576
G: 98% confidence level, value = 2.326
H: 95% confidence level, value = 1.96
I:  90% confidence level, value = 1.645

Formulas (AER Mode):

1;  2.576 STO F 2.326 STO G 1.96 STO H 1.645 STO I ◣
2;  f(A,B,C,J)=A-JB÷√C STO D, A+JB÷√C STO E

Instructions (COMP Mode):

1.  Initialize by pressing [ 1; ].  When the display says ANS1 = 0, the initialization is complete.
2.  Press [ 2; ], enter mean for A, press [ COMP ], enter variance for B, press [ COMP ], enter n for C, press [ COMP ], choose F, G, H, or I for J (confidence level), press [ COMP ].

Examples:

Example 1:
99% level with mean = 34.56, variance = 19.79, n = 53.  For 99%, enter F for J.
Result: 22.557490316, 41.562509684

Example 2:
90% level with mean = 100, variance = 12, n = 42.  For 90%, enter I for J.
Result:  96.9540518717, 103.045948128

Sum of a Function

On the EL-5100, we will have to manually keep track of the loop.

∑ f(I) from I=A to B (increment 1), result is stored in M.


Formula Template (AER Mode):

1;  f(I)= STO I, 0 →M ◣
2; [enter function here] M+, 1+I STO I

Instructions (COMP Mode):

1.  Press [ 1; ].  At the f(I)= prompt, store the lower limit.  Press [ COMP ] twice to complete the initialization.  
2.  Press [ 2; ].   The first result is f(I).  Press [ COMP ] to increase I by 1.  Repeat the pattern by pressing [ COMP ]. Do this until ANS2 > B (you need to keep track manually)
3.  Press [ RM ] to get the final result.

Example:  

∑( (I-2)×(I+6) ) for I=1 to 5

Setup (AER Mode):

1;  f(I)= STO I, 0 →M ◣
2;  (I-2)×(I+6) M+, 1+I STO I

[1; ] [COMP] [COMP]
[2; ] [COMP] [COMP]  ANS2 = 2
[2; ] [COMP] [COMP]  ANS2 = 3
[2; ] [COMP] [COMP]  ANS2 = 4
[2; ] [COMP] [COMP]  ANS2 = 5
[2; ] [COMP] [COMP]  ANS2 = 6
[ RM ]

Result: 55

Fun to explore different ways to solve problems, and play with retro calculators. 

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

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