Saturday, December 15, 2018

TI-60: Triangle Numbers

TI-60:  Triangle Numbers

Introduction

The following program calculates T_n, the nth triangle number.  Triangle numbers are determined by the sum:

T_n = ∑k, from k = 0 to n

The TI-60 does not have either comparison commands or a goto command.  Luckily for the TI-60 (not the case for the TI-55 III), the RST sends the program pointer back to the first step (Step 00) and continues to execute.

We simulate a loop by counting down, when the counter reaches -1, the square root function will cause an error, forcing execution to stop.  You'll see this trick towards the end of the program.

Instructions:

1.  In RUN mode (outside of LRN), store the following values:

R0 = 0 
R1 = n

2.  Execute the program by pressing [RST], [R/S].  The program is done when you see "Error".

3.  Clear the error by pressing [CE/C].

4.  Recall R0.  This is your triangle number.  (R1 will have -1).

TI-60 Program: Triangle Numbers

PC00  OP71:  RCL 
PC01  OP01:  1
PC02  OP61:  STO 
PC03  OP85:  +
PC04  OP00:  0     // sum R1 in R0
PC05  OP75:  -
PC06  OP01:  1
PC07  OP95:  =
PC08  OP61:  STO
PC09  OP01:  1    // store R1 -1 in R1
PC10  OP86:  √  // square root of R1, if less than 0, program stops<0 ending="" error="" font="" loop="" occurs="" the="">
PC11  OP22:  RST  // reset back to step 00

Examples:

T_5 = 15  (0 [STO] 0,  5 [ST0] 1, [RST] [R/S], [CE/C]  [RCL] 0)

T_35 = 630  (in about 45 seconds)

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

No comments:

Post a Comment

HP 42S and TI-60: Dimensions of a Race Track

HP 42S and TI-60:  Dimensions of a Race Track We have a race track that consists of two rectangular tracks connected by a circular ri...