MS Calculator gives different answers

[zerodae]

If I copy paste the following line into calculator (Manually entering the numbers yields same result):
1316*57000+85*142500=

I get different answers.

If the calculator is in standard mode, I wrongly get
10689222112500

If it is in any other mode, I correctly get
87124500


This is not a troll. No really, it isn't.

It happens on a rather clean install of Windows 7 Home Premium 64 bit: one on an Intel Q6600 the other on a brand new mobile AMD Athlon laptop. I have an Ultimate 32bit version that I have not tried yet.

It scares me that this is reproducible on two machines and I cannot find a meaningful relationship between the two numbers. Can someone confirm or explain it?

//Zerodae

 

[pebbly]

Can confirm its true, cannot explain why

 

[rap33042]

I just tried it and get the correct answer no matter the mode

 

[Kari]

I've noticed this earlier.

Calculator makes a mistake in which order different calculations should be made. As everyone knows, that example of yours should be calculated so that both multiplications should be done first (1316*57000 = 75,012,000 and 85*142500 = 12,112,500), and the addidition thereafter (75,012,000 + 12,112,500 = 87124500).

However, calculator forgets the laws of mathematic and makes the calculations in order they are presented (1316*57000 = 75,012,000 > 75,012,000 + 85 = 75,012,085 > 75,012,085 * 142,500 = 10689222112500).

This is not only Windows 7 Calculator issue. It's the same in XP and Vista aswell. In fact, every basic calculator makes this mistake, try if you don't believe me. Calculators working in basic mode do not understand the complexity of a mathematical formula, they do the calculations in the order they are given, not following the laws of mathematics where multiplication preceeds addition.

Kari

 

[zerodae]

Interesting. I cannot believe someone thought that it was a good idea to be different than every other calculator in the world; even my Casio from the last century knows order of operations. Nor that the standard mode would ignore the parens to make it understand order of operations. But I do not remember ever hitting this problem in XP.

Guess I will never use standard mode from now on. Thanks for the insight.

 

[imeem]

BEDMAS

 

[Kari]

Interesting. I cannot believe someone thought that it was a good idea to be different than every other calculator in the world; even my Casio from the last century knows order of operations. Nor that the standard mode would ignore the parens to make it understand order of operations. But I do not remember ever hitting this problem in XP.

Guess I will never use standard mode from now on. Thanks for the insight.

That is not so. As i mentioned in my previous post, almost all basic calculators make the same mistake. I just tested with 4 real calculators I found from our household, three normal basic ones make the same mistake, aswell as did my Logitech MediaPad's calculator. Only a Casio scientific calculator got it right.

However, this is a minus to Microsoft; I just checked Mac OSX, Solaris Unix and SUSE Enterprise Linux calculators in basic mode, they all get it right.

Is it a bug then? I honestly don't know. The calculator in Windows calculates exactly in that order the calculations are input to it, so in that sense it does what's asked.

Kari

 

[logicearth]

You have to remember something, when using the standard/basic mode you are responsible for putting the order in correctly. It works on one input at a time like all calculators do. You input a number and a second it will instantly give you the output if you push equals (=) or another operator. This emulates the majority of real world calculators.

This is not a bug it is working how it should be working. If you need it to process the equation before giving a number back use another mode like scientific. Otherwise, the standard mode is working like it should be. It is not a mistake.


Here is what the calculator sees when you input the numbers: Each line is a new input. (equals how the calculator sees it)
1316*57000+85*142500=

1316

*

57000

+ (75,012,000)

85 (75,012,000 + 85)

* (75,012,085)

142500 (75,012,085 * 142500)

= 10,689,222,112,500

This works like every "single input" calculator I have ever used. Only calculators like my Casio fx-300ES that takes the whole equation before calculating takes the order of operations into consideration.

 

[HerrKaLeun]

Growing up in communist East Germany, we starteed to have calcualtors in school in 7th grade, which was about 1988. Those were capable to calculate correctly.

Shame on MS and all the cheap calculator manufacturers that they still haven't figured it out. However, my $ 15 Casio 115 can calculate correctly.

 

[Kari]

Growing up in communist East Germany, we starteed to have calcualtors in school in 7th grade, which was about 1988. Those were capable to calculate correctly.

My dear wife Angie was also born and raised here in Leipzig, in communist East Germany. One of the calculators I tested as mentioned in my last post was one of her old "Made in Soviet Union" ones. It makes the same mistake as Windows calculator.

Shame on MS and all the cheap calculator manufacturers that they still haven't figured it out. However, my $ 15 Casio 115 can calculate correctly.

As Logiearth said, basically Windows calculator calculates correctly. It does calculations in exact order they are input. You have to remember the basic mode calculator counts every click of add, substract, multiply and divide buttons not only as the function of that button, but it is also thought to be equals (=) function for preceeding calculation.

For instance in 1315 * 57,000 + 85 * 142,000, when you press + 85, the press of + sign is for basic mode calculator first as equals (=) for the first calculation and only after that to mark an addition. (Sorry, New Year's Eve and the amount of whisky in my blood at the moment makes this really confusing and difficult to explain in a foreign language... )

I think if you watch this video carefully you can understand calculator is doing just as it is asked to do:



Kari

 

[HerrKaLeun]

Growing up in communist East Germany, we starteed to have calcualtors in school in 7th grade, which was about 1988. Those were capable to calculate correctly.

My dear wife Angie was also born and raised here in Leipzig, in communist East Germany. One of the calculators I tested as mentioned in my last post was one of her old "Made in Soviet Union" ones. It makes the same mistake as Windows calculator.

Shame on MS and all the cheap calculator manufacturers that they still haven't figured it out. However, my $ 15 Casio 115 can calculate correctly.

As Logiearth said, basically Windows calculator calculates correctly. It does calculations in exact order they are input. You have to remember the basic mode calculator counts every click of add, substract, multiply and divide buttons not only as the function of that button, but it is also thought to be equals (=) function for preceeding calculation.

For instance in 1315 * 57,000 + 85 * 142,000, when you press + 85, the press of + sign is for basic mode calculator first as equals (=) for the first calculation and only after that to mark an addition. (Sorry, New Year's Eve and the amount of whisky in my blood at the moment makes this really confusing and difficult to explain in a foreign language... )

I think if you watch this video carefully you can understand calculator is doing just as it is asked to do:



Kari

no, calculating correctly means obeying the "multiply before adding" rule. This is math. doing it in a different way is wrong.

I've never seen Soviet calculators, but imagine them to be bad... East Germany was the "silicon Valley" of the communist world. "Robotron" was the computer manufacturer and the calculator was made by robotron (I think, but it is all governemnt owned anyway). Every single student from 1987 on used the "SR 1". I believe it stands ofr "Schul Rechner". It was highly subsidized they told us it cost 700 Mark (which was a month salary of an industrial worker) and students could get it for 123 Mark (don't quote me on the actual number)

 

[logicearth]

no, calculating correctly means obeying the "multiply before adding" rule. This is math. doing it in a different way is wrong.

Thus you the user must input the calculation in the correct order. Almost every single calculator that I used that only took one input at a time required the user to put the order correctly. It has worked this way forever.

I'm going to have to guess all your math problems as a student were pre-ordered. Unless the calculator you were given took the whole equation before calculating.

 

[Golden]

This could be easily solved by MS implementing an RPN (Reverse Polish Notation) option in their calculators.

Practical implications

• Calculations occur as soon as an operator is specified. Thus, expressions are not entered wholesale from right to left but calculated one piece at a time, most efficiently from the center outwards.
• The automatic stack permits the automatic storage of intermediate results for use later: this key feature is what permits RPN calculators to easily evaluate expressions of arbitrary complexity: they do not have limits on the complexity of expression they can calculate, unlike algebraic calculators.
• Brackets and parentheses are unnecessary: the user simply performs calculations in the order that is required, letting the automatic stack store intermediate results on the fly for later use. Likewise, there is no requirement for the precedence rules required in infix notation.
• In RPN calculators, no equals key is required to force computation to occur.
• RPN calculators do, however, require an enter key to separate two adjacent numeric operands.
• The machine state is always a stack of values awaiting operation; it is impossible to enter an operator onto the stack. This makes use conceptually easy compared to more complex entry methods.
• Educationally, RPN calculators have the advantage that the user must understand the expression being calculated: it is not possible to simply copy the expression from paper into the machine and read off the answer without understanding. One must calculate from the middle of the expression, which is only meaningful if the user understands what they are doing.
• Reverse Polish notation also reflects the way calculations are done on pen and paper. One first writes the numbers down and then performs the calculation. Thus the concept is easy to teach.
• The widespread use of electronic calculators using infix in educational systems can make RPN impractical at times, not conforming to standard teaching methods. The fact that RPN has no use for parentheses means it is faster and easier to calculate expressions, particularly the more complex ones, than with an infix calculator, owing to fewer keystrokes and greater visibility of intermediate results. It is also easy for a computer to convert infix notation to postfix, most notably via Dijkstra's shunting-yard algorithm – see converting from infix notation below.
• Users must know the size of the stack, since practical implementations of RPN use different sizes for the stack. For example, the algebraic expression
  
  , if performed with a stack size of 4 and executed from left to right, would exhaust the stack. The answer might be given as an erroneous imaginary number instead of approximately 0.5 as a real number.
• When writing RPN on paper (something which even some users of RPN may not do) adjacent numbers need a separator between them. Using a space is not good practice because it requires clear handwriting to prevent confusion. For example, 12 34 + could look like 123 4 + but in a monospace font it is quite clear, while something like 12, 34 + is straightforward. The comma becomes a virtual Space key.
• RPN is very easy to write and makes practical sense when it is adopted. The "learning" process to adopt RPN in writing usually comes later than adopting RPN on a calculator so that one may communicate more easily with non-RPN users.

Reverse Polish notation - Wikipedia, the free encyclopedia

 

[logicearth]

This could be easily solved by MS implementing an RPN (Reverse Polish Notation) option in their calculators.

Why when you can just switch to the Scientific mode? Leaving the simple/standard mode as is keeps it synced with real world calculators. For example if you had an expression like this: 20 * ( 100 + 50 ), the user would still have to order it so 100 + 50 was first because there is no parentheses in standard mode.

 

[Golden]

Fair enough. I guess its my own personal preference for RPN.

Using RPN notation, the result requires:
20
<enter>
100
<enter>
50
<+>
<x>

Using algebraic notation, the result requires:
100
+
50
=
x
20
=

With RPN stacks, I'm not required to calculate 100+50 first, only to remember the basic precedence.