Hewlett-Packard HP-30S

Datasheet legend
Ab/c: Fractions calculation
AC: Alternating current
BaseN: Number base calculations
Card: Magnetic card storage
Cmem: Continuous memory
Cond: Conditional execution
Const: Scientific constants
Cplx: Complex number arithmetic
DC: Direct current
Eqlib: Equation library
Exp: Exponential/logarithmic functions
Fin: Financial functions
Grph: Graphing capability
Hyp: Hyperbolic functions
Ind: Indirect addressing
Intg: Numerical integration
Jump: Unconditional jump (GOTO)
Lbl: Program labels
LCD: Liquid Crystal Display
LED: Light-Emitting Diode
Li-ion: Lithium-ion rechargeable battery
Lreg: Linear regression (2-variable statistics)
mA: Milliamperes of current
Mtrx: Matrix support
NiCd: Nickel-Cadmium rechargeable battery
NiMH: Nickel-metal-hydrite rechargeable battery
Prnt: Printer
RTC: Real-time clock
Sdev: Standard deviation (1-variable statistics)
Solv: Equation solver
Subr: Subroutine call capability
Symb: Symbolic computing
Tape: Magnetic tape storage
Trig: Trigonometric functions
Units: Unit conversions
VAC: Volts AC
VDC: Volts DC
Years of production: 2000-present Display type: Numeric display  
New price: USD 15.99   Display color: Black  
    Display technology: Liquid crystal display 
Size: 6"×3"×½" Display size: 10+2 digits
Weight: 5 oz    
    Entry method: Algebraic with precedence 
Batteries: 2×"LR44" button cell Advanced functions: Trig Exp Hyp Lreg Solv Ab/c Cmem BaseN 
External power:   Memory functions:
    Programming model: Formula programming 
Precision: 24 digits Program functions:  
Memories: 11 numbers Program display: Formula display  
Program memory: 80 bytes Program editing: Formula entry  
Chipset: Kinpo SPLB31A   Forensic result:  

hp30s.jpg (26759 bytes)According the Hewlett-Packard, this calculator is not a programmable model. I have to respectfully disagree: the ability to store an equation and recall it later for evaluation is precisely what makes a calculator programmable. Not very programmable mind you: there are no conditional instructions, loop constructs, subroutines, the ability to store multiple programs, etc. Even so, calculators much more primitive than the HP-30S were called programmable by their respective manufacturers, so the HP-30S definitely belongs in this category.

The HP-30S is one of HP's latest models, one that can be considered part of an overall attempt to re-enter the calculator field that has been all but dominated by HP's competitors, most notably Texas Instruments, Casio, and Sharp in recent years. The HP-30S is a "cheap" scientific calculator; I picked mine up for 20 Canadian dollars the other day at a large electronics store.

My first impression: I long for that era where the quality of a product or its documentation mattered more than its cosmetic appearance. HP used to be famous for their top quality manuals; now all we get is two flimsy sheets and a small quick reference card (mind you, even this is more than you get with most other manufacturers' products!). What you do get instead is faceplates of three different color packaged with the machine...

At least it appears that HP resisted the temptation to package a generic scientific calculator chip under its own brand name. At least that's what I thought when I first encountered this seemingly unique machine. Alas, the machine turns out to be not so unique after all: it is part of a lineup by Kinpo, and may have also been sold under the Citizen and/or Truly brand names.

One particularly interesting feature is that this machine uses binary arithmetic to perform floating point calculations. What? But you thought all calculators used binary logic, right? Well, almost. Most calculators since time immemorial (i.e., since the mid 1960s when the first electronic desktop calculators appeared) used BCD (Binary Coded Decimal) arithmetic that made it relatively easy to convert internally represented values for display purposes and vice versa.

How do I know that the HP-30S uses binary arithmetic? Take the value of Pi for instance. The manual (if it can be called that) states that the calculator uses up to 24 digits of precision. But when I subtract numeric values from the symbolic constant Pi, the result indicates there might be more digits:



So it seems that the calculator "knows" more than 24 digits of Pi: 3.14159265358979323846264917309898...

But there's something wrong here. You see, these aren't the digits of Pi. The correct value is 3.14159265358979323846264338327950...

So the manual was correct after all... we have 24-digit accuracy. But what are these extra digits, then? Where do they come from?

If you're familiar with the representation of floating-point numbers in various number bases, you already know the answer: it is rounding error. A number that can be accurately represented in one number system may require an infinite number of fractional digits in another. For instance, the number 0.13 in base 3 can only be represented as 0.33333333... in base 10. In this case, I suspect that the calculator stores Pi internally as 3.243F6A8885A308D3132hex, and what we see on the display is, in fact, the result of a rounded conversion to the decimal number base.

Since the HP-30S has no built-in Gamma function, my favorite programming example may even prove to be useful. So here is not one, but two implementations of the logarithm of the Gamma function for the HP-30S. The first version uses the extended Stirling formula:

Ans ln(Ans)-Ans+ln(√(2π/Ans))+((((1/99Ans²-1/140)/Ans²+1/105)/Ans²-1/30)/Ans²+1)/12Ans

The second version uses the Lanczos approximation and requires that you preload four variables with the necessary values:


Both implementations are fairly accurate; the advantage of using Stirling's formula is that it uses no extra variables, whereas the Lanczos approximation remains accurate for small (<5) arguments where Stirling's formula fails.

In both cases, the formula should be loaded into the EQN variable; when recalled and executed, it uses the result of the most recent calculation (i.e., the contents of the Ans variable) as its argument.