hp 41c

rather than dot matrix, the display is a segmented lcd with additional segments so as to be able to display letters and a wide range of punctuation and other symbols. programs and functions could be given names and data input and output could be mixed with text. the user mode meant that your own programs could be attached to the keyboard rather than having to be called up by name.

the 41c has 63 registers' worth of storage. registers can be traded with program steps so that between 200 to 400 fully-merged steps are available. the initial setting is 46 program registers and 17 register memories.

the unit is highly expandable. on the top there are four sockets for expansion packs. these packs can have additional memory, rom programs or allow connection of custom peripherals like the card reader and the bar code wand.

programmatically it was excellent. an extensive function catalog, labels (global and local), subroutines (up to 6 deep), a wide selection of conditional branches, loop control (isg, dse), flags, indirect addressing and far easier debugging and editing due to the alphanumeric display of instructions.

the user manual introduces the machine thus,

the hp-41c and hp41-cv calculators represent a totally new concept in the design of hewlett-packard calculators. in fact, because of their advanced capabilities, these calculators can even be called personal computing systems.

with so many kinds of calculator users and applications in the world, we at hewlett-packard decided we could provide a significant contribution by designing and building quality calculators with expandable and flexible capabilities. the alphanumeric hp-41c and hp-41vc calculators are the results of that decision.

program example: sums of reciprocal powers

most people know that 1+1/2+1/3+1/4+... + 1/n diverges as n increases, but the sums of reciprocal squares converges. ie 1+1/(2^2)+1/(3^2)+1/(4^2)+... +1/(n^2) as n increases. the latter series converges to pi^2/6 in the limit.

more generally, we have z(s) = 1/(1^s)+1/(2^s)+1/(3^s)+... + 1/(n^s)
when s > 1, z(s) converges.

here is a program to calculate z(s) for s >= 2.