I haven't ever talked much about the HP33s!
It's the most expensive pure scientific (not graphing) calculator available now, but what features does it have above a $15 calculator, like say the Sharp 506w?
Build-
The calculator does use plastic in its construction, but the front plate is made of brushed aluminum. It consequently feels more solid and sturdy than a cheap calculator. Also, it has rubber grips on the side, making it quite comfortable to hold. It also comes with a (fake) leather case, which is kind of nice. The slots for the 506w's plastic case started cracking apart after awhile.
RPN-
Most calculators use some sort of algebraic entry system, and many of these systems are completely different from each other. (For example, the two line system most use now is a fairly new thing)
Some RPN fans have claimed that most people automatically really try to use even an algebraic calculator to be like RPN, meaning, after doing so many steps in a calculation, eventually you start using the ANS[wer] memory to do one calculation at a time, in a chain. I know that that's how I usually use an algebraic calculator (though the 506w and TI89 allow such long entry lines that it might finally be possible to do a lot of problems with one long list of functions and one press of the equals button); ANS and = are probably the most commonly used buttons.
So, RPN is an alternative entry method that first seems very weird, but increasingly seems more and more natural, and eventually will probably be prefered. It uses a stack of four numbers, and operations work on either the first (for exp or sin, etc.) or first two (for arithmetic) numbers. The two extra levels of the stack automatically store intermediate results, so you can do long or complex calculations without parenthesis. You might be worried about having so many intermediate results that they get pushed off the 4th level. People have claimed that this never happens to RPN experts... which of course is no help at all if you're learning the system. But if you're worried about losing a result, you can always store it in a variable. Even the 506w gives some variables that will most likely be used as a scratch pad area, and the 33s offers many more variables.
It turns out that most operations use fewer keystrokes with RPN, too. For one thing, you don't have to hit equals at the end; you just hit Enter once (usually) at the beginning to get the ball rolling.
RPN also has a "copy down" feature that makes constant calculations (say, adding 2 over and over to a number) easy.
There's no reason a cheap calculator couldn't use RPN (in fact, it'd probably be easier: You only have to store 4 numbers rather than numbers and pending operations, as with an algebraic. This is one reason why the first scientific calculator used RPN), but so far I don't believe any ever has.
Programmability-
I don't think any cheap or non-HP scientific calculator in America has ever been programmable. (some import Casios have been, but are probably much simplier than the 33s) So, this is a nice feature.
The programming language is supposed to be an automated version of what you'd type while using the calculator manually ("keystroke programming"). It supports branching (with GTO), loops, input, output, and generally any programming fundamentals you'd expect.
There also are Checksums to verify correct program entry.
The calculator is probably best used for programming simple but repetitive tasks, but it is possible to make more complex programs.
Intelligent key layout-
The key layout is something all calculators have to deal with, and I think most have evidence of some thought put into them. Eventually, with too many functions, it's impossible to put all of the most used functions on a face key, and compromises have to be made. For instance, the 506w has pi, reciprocal, and ANS as shifted keys, and I'd prefer all of those to be face.
One thing I like about the 33s's layout (and I've never used another calculator like this) is that both Exp and Ln are face keys, while the base ten logs are shifted (usually, Ln and Log are the face keys). I used natural functions MUCH more than common functions (usually, the only time I'll take a base ten log is if I want to convert a number to scientific notation but don't want to change the calculator mode, and don't trust a simple counting of the digits). I also use squareroots and squares with almost equal frequency, and both of those are face (I think the 506w has square and cube as face keys, and square- and cube-root as shifted) Almost all of the commonly used functions are face functions, which, together with RPN, makes the calculator quick to use. Because it's RPN, there is no need for an ANS key (EVERY function automatically works on ANS). One face function I rarely use is the universal root key -- it's just about as easy to 1/x and universal power. And pi is a shifted function, but oh, well.
Improved Display-
If you look at the 506w from an extreme angle, all the segments will be filled in. The 33s allows viewing from wider angles with little to no loss of contrast (there is some amount of shadowing). Also, the display for both lines is dot matrix. This allows programming commands to be displayed as text.
Constants Library-
The 506w has a constants library, but it's not as nice as the 33s's. It's not the sheer number of constants -- for significant constants, their libraries probably overlap; the 506w might have more total, but the extras are probably trivial (eg., 1x10^-3 is one).
The nice thing about the 33s is that the library is a menu that shows the symbol in the upper row, and the number in the bottom. You can use the arrow keys to scroll through them.
There's no reason the 506w couldn't have done it this way (it has a dot matrix upper line display, and arrow keys), but it didn't. Instead, you have to enter a 2 digit code to get the desired constant. How do you know the code? Well, it's printed on a card that's supposed to fit in the calculator's case, but as I mentioned, the case has cracked so I don't use it anymore. So, you might need to just step through all the different codes until you find the constant you want. And for that to work, you have a pretty good idea of the constant's value, or the keycode, anyway.
-The Manual
The manual is beyond compare of all current scientific calculators, and even most graphing! It looks to be about 300 pages long, and is very nice. It covers everything about operating the calcutor in good deal. It's actually kind of fun to work through the RPN calculation examples, and it's almost even sort of thrilling to get to the end of a long calculation and realize you hadn't pushed an important number off the stack.
Plus, the back of the manual contains some good programs, such as a polynomial solver that finds all real and imaginary roots of up to a 5th degree equation.
Equation mode-
You can store an almost unlimited number of equations. Equations can be substituted into and evaluated, or solved, or integrated. Equations can also be used in programs (which makes them more readable than RPN instructions). The equation mode uses algebraic input. If you insist on RPN, RPN programs that act like functions can also be integrated or solved.
Equations also have checksums.
Otherwise, much of the 33s's capabilities are similar to a current scientifics. It includes, for example, numerical solving and integration. There are some minor improvements and issues. I like that factorial can be used with nonintegers. You do need menus for the linear regression features, but they don't take much time to go through, and are well organized and labeled. The calculator shows 12 digits at a time (IIRC) while most only show 10, but it seems to store no extra digits internally. It also allows numbers up to 10^500, while most scientifics go to 10^100.
The fraction mode has advantages and disadvantages. Advantage: Can approximate a number with a fraction. Example: Can give pi ~ 355/113. Most calculators will only convert a number to a fraction if that number is EXACTLY equal to that fraction. For the 506w, it won't convert 0.333333333 to 1/3!! ALL the internal digits also have to match up to 1/3.
On the other hand, the fraction mode is purely a display or approximating mode. It doesn't actually store 1/3 as 1/3, but as 0.3333..., and merely displays 1/3. So, in principle I guess accuracy could be lost.
So, what's missing?
Number Bases-
Actually, the calculator does support some different number bases, and in fact supports a huge word size for binary numbers; much larger than any other scientific I've seen (it shows the digits in different "windows" that can be scrolled through).
But it has no bitwise (AND, OR, etc) operations. Very strange!
Matrices-
No built in matrix support whatsoever. The 506w has some level of matrix support (up to four 4x4 matrices -- why not up to one single 8x8? It's the same number of entries)
Complex numbers-
Complex number support is mixed. On the one hand, not only is arithmetic supported, but some scientific functions are as well: EXP, LN, SIN, etc. Also, you don't need to change modes to use complex numbers.
On the other hand, while SIN is supported, Arcsin is not! (generally, no shifted function is supported). And why isn't complex squareroot supported? (instead, you have to raise to the 0.5 power).
Also, the calculator does not use a complex stack. The four stack levels are divided up into the real and imaginary parts of two numbers. So, you can only deal with 2 complex numbers at a time. Complicated calculations WILL require much variable manipulation.
...OR, you could go to algebraic mode. There, you can enter rather arbitrarily complicated expressions with complex numbers. It's just about the only use for algebraic mode I've found. It's still not the best solution (the 33s's algebraic mode is sort of crippled compared to the 506w's. It has little editing)
-Built in abilities
The 506w has built in linear, exponential, power, reciprocal and quadratic regression. The 33s only has linear. The manual does have a program that gives the other forms.
The 506 has built in support for up to 3x3 linear systems (and 4x4 should be easy in matrix mode). The 33s has no built in support for linear systems, and I already mentioned matrices. The manual does have a program for a 3x3 system. It's possible to write a program that could solve up to a 7x7 system.
The 506w has built in support for solving quadratics and cubics (including complex roots). The 33s doesn't have this built in, but as I said, the manual has a program that can go up to 5th degree.
Memory and variables-
This is only a concern when compared to other HP or graphing calculators.
There is support for 26 (A-Z) normal variables, plus a few more (eg., for statistics). This is huge compared to the 506w, but small compared to the 15c's 64. It puts a limit on the size of a matrix that programs could theoritically use.
Personally, I don't think this is much of a problem.
The calculator has 31 KB of memory, which is HUGE for a scientific. (Some older HP's only had about 0.5 KB). So, what's the problem?
You won't be able to fill that memory with programs. There is a limit of 26 "labels". All programs fit in the same "program space": Basically, it's like there's only one program, divided into different subroutines. Of course, you can have more than one program, if the subroutines are self contained and have a RTN (return) command so they don't run into each other.
But every program OR subroutine takes a label. That a program takes a label probably isn't a big deal; that a subroutine does probably is. You cannot GOTO an arbitrary line number, only to one of the 26 labels. So, every time a program has to branch, you'll use a label, and you'll find that many programs will use multiple labels, and the 26 will get used up quickly.
On the other hand, if you love the equation mode, you might get some use out of the 31KB. There's almost no limit on the number of equations you can store.
Also, there are hacks to save labels or get more use out of memory even in program mode.
"Perhaps one did not want to be loved so much as to be understood."
-Orwell
It's the most expensive pure scientific (not graphing) calculator available now, but what features does it have above a $15 calculator, like say the Sharp 506w?
Build-
The calculator does use plastic in its construction, but the front plate is made of brushed aluminum. It consequently feels more solid and sturdy than a cheap calculator. Also, it has rubber grips on the side, making it quite comfortable to hold. It also comes with a (fake) leather case, which is kind of nice. The slots for the 506w's plastic case started cracking apart after awhile.
RPN-
Most calculators use some sort of algebraic entry system, and many of these systems are completely different from each other. (For example, the two line system most use now is a fairly new thing)
Some RPN fans have claimed that most people automatically really try to use even an algebraic calculator to be like RPN, meaning, after doing so many steps in a calculation, eventually you start using the ANS[wer] memory to do one calculation at a time, in a chain. I know that that's how I usually use an algebraic calculator (though the 506w and TI89 allow such long entry lines that it might finally be possible to do a lot of problems with one long list of functions and one press of the equals button); ANS and = are probably the most commonly used buttons.
So, RPN is an alternative entry method that first seems very weird, but increasingly seems more and more natural, and eventually will probably be prefered. It uses a stack of four numbers, and operations work on either the first (for exp or sin, etc.) or first two (for arithmetic) numbers. The two extra levels of the stack automatically store intermediate results, so you can do long or complex calculations without parenthesis. You might be worried about having so many intermediate results that they get pushed off the 4th level. People have claimed that this never happens to RPN experts... which of course is no help at all if you're learning the system. But if you're worried about losing a result, you can always store it in a variable. Even the 506w gives some variables that will most likely be used as a scratch pad area, and the 33s offers many more variables.
It turns out that most operations use fewer keystrokes with RPN, too. For one thing, you don't have to hit equals at the end; you just hit Enter once (usually) at the beginning to get the ball rolling.
RPN also has a "copy down" feature that makes constant calculations (say, adding 2 over and over to a number) easy.
There's no reason a cheap calculator couldn't use RPN (in fact, it'd probably be easier: You only have to store 4 numbers rather than numbers and pending operations, as with an algebraic. This is one reason why the first scientific calculator used RPN), but so far I don't believe any ever has.
Programmability-
I don't think any cheap or non-HP scientific calculator in America has ever been programmable. (some import Casios have been, but are probably much simplier than the 33s) So, this is a nice feature.
The programming language is supposed to be an automated version of what you'd type while using the calculator manually ("keystroke programming"). It supports branching (with GTO), loops, input, output, and generally any programming fundamentals you'd expect.
There also are Checksums to verify correct program entry.
The calculator is probably best used for programming simple but repetitive tasks, but it is possible to make more complex programs.
Intelligent key layout-
The key layout is something all calculators have to deal with, and I think most have evidence of some thought put into them. Eventually, with too many functions, it's impossible to put all of the most used functions on a face key, and compromises have to be made. For instance, the 506w has pi, reciprocal, and ANS as shifted keys, and I'd prefer all of those to be face.
One thing I like about the 33s's layout (and I've never used another calculator like this) is that both Exp and Ln are face keys, while the base ten logs are shifted (usually, Ln and Log are the face keys). I used natural functions MUCH more than common functions (usually, the only time I'll take a base ten log is if I want to convert a number to scientific notation but don't want to change the calculator mode, and don't trust a simple counting of the digits). I also use squareroots and squares with almost equal frequency, and both of those are face (I think the 506w has square and cube as face keys, and square- and cube-root as shifted) Almost all of the commonly used functions are face functions, which, together with RPN, makes the calculator quick to use. Because it's RPN, there is no need for an ANS key (EVERY function automatically works on ANS). One face function I rarely use is the universal root key -- it's just about as easy to 1/x and universal power. And pi is a shifted function, but oh, well.
Improved Display-
If you look at the 506w from an extreme angle, all the segments will be filled in. The 33s allows viewing from wider angles with little to no loss of contrast (there is some amount of shadowing). Also, the display for both lines is dot matrix. This allows programming commands to be displayed as text.
Constants Library-
The 506w has a constants library, but it's not as nice as the 33s's. It's not the sheer number of constants -- for significant constants, their libraries probably overlap; the 506w might have more total, but the extras are probably trivial (eg., 1x10^-3 is one).
The nice thing about the 33s is that the library is a menu that shows the symbol in the upper row, and the number in the bottom. You can use the arrow keys to scroll through them.
There's no reason the 506w couldn't have done it this way (it has a dot matrix upper line display, and arrow keys), but it didn't. Instead, you have to enter a 2 digit code to get the desired constant. How do you know the code? Well, it's printed on a card that's supposed to fit in the calculator's case, but as I mentioned, the case has cracked so I don't use it anymore. So, you might need to just step through all the different codes until you find the constant you want. And for that to work, you have a pretty good idea of the constant's value, or the keycode, anyway.
-The Manual
The manual is beyond compare of all current scientific calculators, and even most graphing! It looks to be about 300 pages long, and is very nice. It covers everything about operating the calcutor in good deal. It's actually kind of fun to work through the RPN calculation examples, and it's almost even sort of thrilling to get to the end of a long calculation and realize you hadn't pushed an important number off the stack.
Plus, the back of the manual contains some good programs, such as a polynomial solver that finds all real and imaginary roots of up to a 5th degree equation.
Equation mode-
You can store an almost unlimited number of equations. Equations can be substituted into and evaluated, or solved, or integrated. Equations can also be used in programs (which makes them more readable than RPN instructions). The equation mode uses algebraic input. If you insist on RPN, RPN programs that act like functions can also be integrated or solved.
Equations also have checksums.
Otherwise, much of the 33s's capabilities are similar to a current scientifics. It includes, for example, numerical solving and integration. There are some minor improvements and issues. I like that factorial can be used with nonintegers. You do need menus for the linear regression features, but they don't take much time to go through, and are well organized and labeled. The calculator shows 12 digits at a time (IIRC) while most only show 10, but it seems to store no extra digits internally. It also allows numbers up to 10^500, while most scientifics go to 10^100.
The fraction mode has advantages and disadvantages. Advantage: Can approximate a number with a fraction. Example: Can give pi ~ 355/113. Most calculators will only convert a number to a fraction if that number is EXACTLY equal to that fraction. For the 506w, it won't convert 0.333333333 to 1/3!! ALL the internal digits also have to match up to 1/3.
On the other hand, the fraction mode is purely a display or approximating mode. It doesn't actually store 1/3 as 1/3, but as 0.3333..., and merely displays 1/3. So, in principle I guess accuracy could be lost.
So, what's missing?
Number Bases-
Actually, the calculator does support some different number bases, and in fact supports a huge word size for binary numbers; much larger than any other scientific I've seen (it shows the digits in different "windows" that can be scrolled through).
But it has no bitwise (AND, OR, etc) operations. Very strange!
Matrices-
No built in matrix support whatsoever. The 506w has some level of matrix support (up to four 4x4 matrices -- why not up to one single 8x8? It's the same number of entries)
Complex numbers-
Complex number support is mixed. On the one hand, not only is arithmetic supported, but some scientific functions are as well: EXP, LN, SIN, etc. Also, you don't need to change modes to use complex numbers.
On the other hand, while SIN is supported, Arcsin is not! (generally, no shifted function is supported). And why isn't complex squareroot supported? (instead, you have to raise to the 0.5 power).
Also, the calculator does not use a complex stack. The four stack levels are divided up into the real and imaginary parts of two numbers. So, you can only deal with 2 complex numbers at a time. Complicated calculations WILL require much variable manipulation.
...OR, you could go to algebraic mode. There, you can enter rather arbitrarily complicated expressions with complex numbers. It's just about the only use for algebraic mode I've found. It's still not the best solution (the 33s's algebraic mode is sort of crippled compared to the 506w's. It has little editing)
-Built in abilities
The 506w has built in linear, exponential, power, reciprocal and quadratic regression. The 33s only has linear. The manual does have a program that gives the other forms.
The 506 has built in support for up to 3x3 linear systems (and 4x4 should be easy in matrix mode). The 33s has no built in support for linear systems, and I already mentioned matrices. The manual does have a program for a 3x3 system. It's possible to write a program that could solve up to a 7x7 system.
The 506w has built in support for solving quadratics and cubics (including complex roots). The 33s doesn't have this built in, but as I said, the manual has a program that can go up to 5th degree.
Memory and variables-
This is only a concern when compared to other HP or graphing calculators.
There is support for 26 (A-Z) normal variables, plus a few more (eg., for statistics). This is huge compared to the 506w, but small compared to the 15c's 64. It puts a limit on the size of a matrix that programs could theoritically use.
Personally, I don't think this is much of a problem.
The calculator has 31 KB of memory, which is HUGE for a scientific. (Some older HP's only had about 0.5 KB). So, what's the problem?
You won't be able to fill that memory with programs. There is a limit of 26 "labels". All programs fit in the same "program space": Basically, it's like there's only one program, divided into different subroutines. Of course, you can have more than one program, if the subroutines are self contained and have a RTN (return) command so they don't run into each other.
But every program OR subroutine takes a label. That a program takes a label probably isn't a big deal; that a subroutine does probably is. You cannot GOTO an arbitrary line number, only to one of the 26 labels. So, every time a program has to branch, you'll use a label, and you'll find that many programs will use multiple labels, and the 26 will get used up quickly.
On the other hand, if you love the equation mode, you might get some use out of the 31KB. There's almost no limit on the number of equations you can store.
Also, there are hacks to save labels or get more use out of memory even in program mode.
"Perhaps one did not want to be loved so much as to be understood."
-Orwell
