Calculation Error In Excel 2007
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Excel Calculation Issue Update by Diego Oppenheimer, on September 25, 2007February 9, 2016 | 0 Comments | 0 Share Yesterday we were alerted to an issue in
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Excel 2007 (and Excel Services 2007) involving calculation of numbers around 65,535. The Excel team would like to provide a description of the issue and explain what we're doing about it. Background Yesterday evening we were alerted to an issue in Excel 2007 (and Excel Services 2007) involving calculation of numbers around 65,535. The first calculate standard deviation excel example that we heard about was =77.1*850, but it became clear from our testing as well as additional reports that this was just one instance where Excel 2007 would return a value of 100,000 instead of 65,535. The majority of these additional reports were focused on multiplication (ex. =5.1*12850; =10.2*6425; =20.4*3212.5 ), but our testing showed that this really didn't have anything do to with multiplication - it manifested itself with many but not all calculations in Excel that should have resulted in 65,535 (=65535*1 and =16383.75*4 worked for instance). Further testing showed a similar phenomenon with 65,536 as well. This issue only exists in Excel 2007, not previous versions. The Problem This issue was introduced when we were making changes to the Excel calculation logic in the Office 2007 time frame. Specifically, Excel incorrectly displays the result of a calculation in 12 very specific cases (outlined below). The key here is that the issue is actually not in the calculation itself (the re
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REPORTING All articles IFRS Internal control Private company reporting SEC compliance and reporting how do you calculate the standard error U.S. compliance and reporting Latest Stories AUDITING All articles Compilation and review Peer review Performing an audit Latest how to calculate error in chemistry Stories MANAGEMENT ACCOUNTING All articles Financial reporting Human resources Planning and budgeting Risk management Strategy and governance Latest Stories Home News Magazine Video Topics Breaking News ColumnTechnology Q&A Bugged by Excel's https://blogs.office.com/2007/09/25/calculation-issue-update/ calculation errors BY J. CARLTON COLLINS, CPA Related TOPICS Information Management and Technology Assurance Q: I found an anomaly with a rather simple Excel computation; specifically, Excel calculates 111,111,111 times 111,111,111 to equal 12,345,678,987,654,300, which is incorrect (the correct answer should end in “21,” not “00”). If Excel’s arithmetic fails, then what else is false, and why does this happen? ( Author’s http://www.journalofaccountancy.com/issues/2014/mar/excel-calculation-errors.html note: You must increase the column width size to view the full number mentioned by the reader; otherwise Excel displays the number in exponential format (1.23457E+16), which does not allow you to see the calculation problem. If Excel continues to display the number in exponential format after you increase the column width, then right-click on the cell, select Format Cells, and in the pop-up box, select Number under the Number tab.) A: You don’t need arithmetic to expose this problem; you can’t even type 12345678987654321 into Excel. When you try, Excel displays 12345678987654300. This is not an anomaly. Excel is designed to handle only 15 total digits in a given number (including digits after the decimal place when applicable). Therefore, it is impossible to accurately type any number into Excel with more than 15 digits (ending in numbers other than zero). If you do, Excel rounds the digits after the 15th place down to zero. This problem stems from the fact that computers store numbers as binary numbers and display them as numeric numbers. The inherent back-and-forth conversion causes problems with certain numbers. Excel follows
you 65,535, was actually displaying 100,000. Before I try to explain this, I should disclose that I did work on the Excel team, but that wasthirteen years ago. I haven't been there for a long http://www.joelonsoftware.com/items/2007/09/26b.html time. I don't even think I know anyone on that team any more. I'm just trying to explain the bug a little bit as a public service. The first thing you have to understand is that Excel https://en.wikipedia.org/wiki/Numeric_precision_in_Microsoft_Excel keeps numbers, internally, in a binary format, but displays them as strings. For example, when you type 77.1, Excel stores this internally using 64 bits: 0100 0000 0101 0011 0100 0110 0110 01100110 0110 0110 0110 0110 error in 0110 0110 0110 The display is showing you four characters: "7", "7", ".", and "1". Somewhere inside Excel is a function that converts binary numbers to strings for displaying. This is the code that has the bug that causes a few numbers which are extremely close to 65,535 to be formatted incorrectly as 100,000. If you use the number further along in calculations, for example, if you add 2 to the results, you'll get the how to calculate right thing. =77.1*850 -> displays 100000 =77.1*850+2 -> displays 65537, correctly. Just to throw people off, this bug also exists for a few numbers which are extremely close to 65,536. They display incorrectly as 100,001. =77.1*850+1 -> displays 100,001, incorrectly. This is still only a bug in the number formatting code; if you try to make a chart with that number in it, you'll get a correct chart. Now... you may have noticed that I said that this bug exists for numbers which are extremely close to 65,535, but not for 65,535 itself. Indeed if you enter 65,535 you see 65,535. But, you notice, 77.1 * 850 should be exactly 65,535, notextremely close to65,535! Look closely at the binary representation for 77.1: 0100 0000 0101 0011 0100 0110 0110 01100110 0110 0110 0110 0110 0110 0110 0110 See how there's a lot of 0110 0110 0110 there at the end? That's because 0.1 has no exact representation in binary... it's a repeating binary number. It's sort of like how 1/3 has no representation in decimal. 1/3 is 0.33333333 and you have to keep writing 3's forever. If you lose patience, you get something inexact. So you can imagine how, in decimal, if you tried to do 3*1/3, and you didn't have time to write 3's forever, the result you would ge
numbers (it has limited precision). Excel nominally works with 8-byte numbers by default, a modified 1985 version of the IEEE 754 specification[1] (Besides numbers, Excel uses a few other data types.[2]) Although Excel can display 30 decimal places, its precision for a specified number is confined to 15 significant figures, and calculations may have an accuracy that is even less due to three issues: round off,[3] truncation, and binary storage. Contents 1 Accuracy and binary storage 2 Examples where precision is no indicator of accuracy 2.1 Statistical functions 2.2 Subtraction of Subtraction Results 2.3 Round-off error 2.4 Accuracy within VBA 3 References Accuracy and binary storage[edit] Excel maintains 15 figures in its numbers, but they are not always accurate: the bottom line should be the same as the top line. Of course, 1 + x − 1 = x. The discrepancy indicates the error. All errors but the last are beyond the 15-th decimal. In the top figure the fraction 1/9000 in Excel is displayed. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using Excel. Because the sum has only eleven 1's after the decimal, the true difference when ‘1’ is subtracted is three 0's followed by a string of eleven 1's. However, the difference reported by Excel is three 0's followed by a 15-digit string of thirteen 1's and two extra erroneous digits. Thus, the numbers Excel calculates with are not the numbers that it displays. Moreover, the error in Excel's answer is not simply round-off error. The inaccuracy in Excel calculations is more complicated than errors due to a precision of 15 significant figures. Excel's storage of numbers in binary format also affects its accuracy.[4] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15-th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number. If this binary version of x is a simple power of 2, the 15-digit decimal approximation to x is stored in the sum, and the top two examples of the figure indicate recovery of x without error. In the third example, x is a more complicated binary number, x = 1.110111⋯111 × 2−49 (15 bits altogether). Here x is approximated by the 4-bit binary 1.111 × 2−49 (some insight