Battle of the “Cheap” Calculators: Sharp EL-501W vs. Bazic 3003
“Let’s Get Ready to Rumble!”
Today is an accuracy battle between the:
Sharp EL-501W
This is brand name calculator. In the 2010s, Sharp manufactured one with blue casing. However, their current EL-501W type (really named the EL-501XBWH) has black casing. Both the EL-501W and EL-501XBWH have the same keyboard and the same amount of functions. The average price runs from $9 to $16 (US).
This is the Bazic 3003, a clone of the Sharp EL-501W/EL-501XBWH. This model sells in discount stores for anywhere from $3 to $6 (US).
There is another clone, the Jot Scientific Calculator which is physically smaller than both models I mentioned, and is even cheaper, close it $1 to $3. (US) I won’t be using this model in today’s tests.
The features on all these models include:
* trigonometric, hyperbolic, logarithm, and power functions
* binary, decimal, octal, and hexadecimal base conversions
* two buttons, [ a ] and [ b ] which assists with complex number arithmetic and polar/rectangular conversions
* random numbers
* one-variable statistics with basic analysis
The Exchange Function: { ↕ }
The exchange key switches the operands in arithmetic calculation. The key sequence is the same: [ 2ndF ] [ ( ] { ↕ }. If we complete an arithmetic calculation by pressing the equals button [ = ], the exchange function recalls the second operand for each operation. Well, almost.
Operation |
Keystrokes |
Result |
Addition |
A [ + ] B [ = ] [ 2ndF ] [ ( ] { ↕ } |
B |
Subtraction |
A [ - ] B [ = ] [ 2ndF ] [ ( ] { ↕ } |
B |
Multiplication |
A [ × ] B [ = ] [ 2ndF ] [ ( ] { ↕ } |
A |
Division |
A [ ÷ ] B [ = ] [ 2ndF ] [ ( ] { ↕ } |
B |
Power |
A [ y^x ] B [ = ] [ 2ndF ] [ ( ] { ↕ } |
B |
(A, B are two arbitrary numbers)
The Sharp EL-501W has plastic keys, a slide case, and takes two LR44 batteries, while the Bazic 3033 has rubber keys, a flip case, and takes two LR1130 batteries. As a personal preference, I prefer plastic keys to rubber keys.
Let’s compare.
A Comparison of Accuracy
The Trigonometric Forensics Evaluation
This test calculates:
arcsin( arccos( arctan( tan( cos( sin( 9° )))))) (six set of parenthesis)
However, we do not need parenthesis:
[ DRG ] (press until degrees mode is set)
9 [ SIN ] [ COS ] [ TAN ]
[ 2ndF ] [ TAN ] {TAN^-1} [ 2ndF ] [ COS ] {COS^-1} [ 2ndF ] [ SIN ] {SIN^-1}
Ideally, the answer returned should be exactly 9.
This test is presented on datamath.org web site (see source below), and this test was used to determine what chips were used in various Texas Instruments calculators.
Results:
Sharp EL-501W |
8.9999 98637 |
Bazic 3003 |
8.9999 9986 |
Bazic gets the slight edge on this test.
The Cube of a Complex Number
The next test calculates (4.5 + 2.2i)^3.
The complex number mode only works for arithmetic functions (+, -, ×, ÷).
First, lets’ calculate the cube in complex mode.
Keystrokes:
[ 2ndF ] [ → ] {CPLX} (until CPLX indicator appears)
4.5 [ a ] 2.2 [ b ] [ × ] 4.5 [ a ] 2.2 [ b ] [ × ] 4.5 [ a ] 2.2 [ b ] [ = ]
Results:
Sharp EL-501W |
25.785 + 123.002i (press [ b ] for the imaginary part) |
Bazic 3003 |
25.785 + 123.002i (press [ b ] for the imaginary part) |
Now in Real Mode using the polar/rectangular conversion functions.
Keystrokes:
[ 2ndF ] [ → ] {CPLX} (until CPLX indicator disappears)
4.5 [ a ] 2.2 [ b ] [ 2ndF ] [ a ] { →rθ }
[ b ] [ x→M/STO ] [ a ] [ y^x ] 3 [ = ] (manually record 125.6756071)
[ RM/RCL ] [ × ] 3 [ = ] [ b ] 125.6756071 [ a ] [ 2ndF ] [ b ] { →xy }
Results:
Sharp EL-501W |
25.78499999 + 123.002i (press [ b ] for the yi part) |
Bazic 3003 |
25.78499999 + 123.002i (press [ b ] for the yi part) |
Test of the Logarithm Bug
This test to check to the accuracy of the approximation of e^x, where
e^x = lim n → ∞ (1 + x / n) ^n
If x = 1, then e = e^x = lim n → ∞ (1 + 1 / n) ^n
This test came about because there were several TI-30X and TI-36X calculators that were manufactured in the 1990s. See the Logarithm Bug in the Sources section for more details.
At various values of n:
(1 + 1 / N)^N |
Sharp EL-501W |
Bazic 3003 |
N = 10 |
2.59374246 |
2.59374246 |
N = 1,000 |
2.716923932 |
2.716923932 |
N = 100,000 |
2.718268237 |
2.718268237 |
N = 10,000,000 = 1E7 |
2.718281693 |
2.718281693 |
Both calculators give the same results. More importantly, there is no “logarithm bug” present from these results. Yay!
Statistics of Large Numbers
Sometimes when doing statistics of large numbers, which the numbers themselves differ by little, accuracy can suffer.
The data points for this sample:
100 008 |
100 014 |
100 007 |
100 016 |
100 009 |
100 006 |
100 010 |
100 015 |
100 012 |
100 018 |
Both calculators give these results:
Mean: 100011.5
Sum: 1000115
Sum^2: 1.0002E+11 (1.000230015E+11)
σx = 3.905124838
sx = 4.116363012
n = 10
Overall, the two calculators return the same result. Based off these results, it’s down to how much money you want to spend and what type of keys do you prefer.
Sources
Woerner, Joerg. “Calculator Integrated Circuits Forensics” Datamath.org. Last updated December 12, 2001
http://www.datamath.org/Forensics.htm. Retrieved March 16, 2024.
Senzer, Bob, Mike Sebastian, and Joerg Woerner. “Logarithm Bug” Datamath.org. Last updated October 11, 2005. http://www.datamath.org/Story/LogarithmBug.htm Retrieved March 16, 2024.
For the Star Wars fans, may the Fourth and Force be with you,
Eddie
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