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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