AKA: CHOOSING AND USING AN ELECTRONIC CALCULATOR,
Date of intro: dec-1973,
Classification: / Documentation / Article,
Publisher-1: 73 MAGAZINE, Publisher-2: STARK Peter A.,
Info: Pages 97–106 discuss how to choose an electronic calculator and how even a relatively simple calculator can be used for more advanced mathematical and electronic calculations.
The author points out that calculator prices were falling quickly in the early 1970s, making them increasingly accessible to hobbyists and radio amateurs.
Choosing a calculator:
Calculators range from simple models that only add, subtract, multiply and divide to expensive scientific calculators.
The article uses the HEWLETT-PACKARD: 45 as an example of a highly advanced calculator.
It could perform trigonometric functions, logarithms, square roots, statistical calculations and various conversions.
However, the author argues that most amateur users do not need such an expensive machine.
When buying a cheaper calculator, several features are important.
Table-top calculators generally have larger displays and keys, while pocket calculators are smaller but may have displays that are harder to read.
Battery life is another consideration, especially because inexpensive calculators may use non-rechargeable batteries.
An especially important choice is between a fixed decimal point and a floating decimal point. Fixed-point calculators are convenient for financial calculations because they can automatically round amounts to cents.
Floating-point calculators are much better for scientific and electronic calculations because they can work with very small values, such as capacitor values.
The author therefore recommends floating point when only one type can be chosen.
Number of digits and calculator capacity:
The number of digits is also important.
Most inexpensive calculators have around eight digits, which the author considers adequate for most serious calculations.
Models with only four or six digits may be cheaper but are much less convenient.
The article also warns that advertising such as ‘8-digit display, 16-digit capacity’ can be misleading.
It does not necessarily mean that the calculator can directly handle 16-digit numbers.
Instead, it may calculate a larger result but only show its most significant digits.
The constant function:
Another useful feature is the constant key.
It allows the same number to be reused in a series of calculations.
For example, a radio amateur can quickly calculate several transmitter crystal frequencies using the same multiplication factor without entering that factor every time.
However, the author notes that although manufacturers heavily advertised this function, it is not useful for every type of calculation.
Useful calculator tricks:
The article then demonstrates several tricks that make simple calculators more powerful.
Some calculators can square a number without entering it twice.
For example, instead of entering the same number twice for multiplication, the user may be able to enter the number followed by multiplication and equals.
A similar trick can calculate a reciprocal (1/x).
Reciprocals are particularly useful in electronics.
The article demonstrates this with the calculation of the equivalent resistance of two resistors connected in parallel.
The author also explains that calculations can often be simplified by choosing appropriate units. For example, instead of entering very large numbers for kilo-ohms or extremely small numbers for microfarads, the calculation can be arranged using relationships such as kilo × milli = 1 and mega × micro = 1.
This prevents an eight-digit calculator from overflowing and makes electronic calculations much easier.
Calculating square roots:
One of the most interesting sections explains how to calculate square roots even if the calculator has no square-root button.
The author introduces the NEWTON–RAPHSON iteration method.
The basic idea is to:
Make an initial guess for the square root.
Divide the original number by that guess.
Average the result with the original guess.
Repeat the process until the answer stops changing.
For example, when calculating SquareRoot 16, the article begins with a guess of 3.
Repeating the process quickly produces values increasingly close to 4.
The same method is demonstrated with SquareRoot 10, which converges to approximately 3.1622776 on an eight-digit calculator.
A better first guess makes the calculation faster, although even a poor guess will eventually produce an accurate result.
For extremely large or small numbers, the article recommends dividing the number into groups or breaking it into simpler factors.
This allows calculations that would otherwise contain too many digits for a basic calculator.
Main idea:
The main message of these pages is that you do not necessarily need an expensive scientific calculator to perform advanced calculations.
Choosing a basic calculator with useful features—especially floating-point operation and enough digits—and learning a few mathematical tricks can make it surprisingly powerful.
The article shows that radio amateurs can use simple calculators for practical electronics problems involving resistance, capacitance, reactance, frequencies, square roots and other engineering calculations.
At the end of page 106, the author begins introducing methods for calculating even more advanced functions such as sine, cosine, tangent and exponentials, which continue on the following pages.