How to use the BITOR function

What is the BITOR function?

The BITOR function performs a bit-wise 'OR' of two decimal numbers, it returns a decimal number as well.

1. Introduction

What is a decimal number?

The decimal system is a positional numeral system that uses 10 as the base, it requires 10 different numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The dot or the decimal point represents decimal fractions which are not whole numbers.

The decimal number 520 has three positions, each with a different weight. It starts with 10^0 on the right and increases by one power on each additional position to the left.

520 = (5*10^2)+(2*10^1)+(0*10^0)

520 = 500 + 20 + 0

What is a bit?

The binary system is a positional numeral system that uses only two digits: 0 and 1. The binary system is important in our society, many devices like computers, digital cameras, mobile phones and modern cars use binary code to store, process and communicate data. The binary numeral system makes it easy to store and transmit data using binary digits or bits.

The following table shows decimal numbers from 0 to 11 and the binary equivalent:

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011

What is bit-wise?

Bit-wise operations are performed on the binary representation of numbers, where each bit has a value of either 0 or 1. Some common bit-wise operations are AND, OR, XOR, NOT and SHIFT. They can be used for masking, toggling, swapping, testing or arithmetic. This article demonstrates OR operations.

What is an OR operation?

The BITOR function performs OR logic bit by bit on the numbers based on their binary representation. OR logic means that the value of each bit position is counted only if at least one parameter's bits at that position are 1.

The following operations show that OR logic is the same as adding binary numbers:

0+0=0
1+0=1
0+1=0
1+1=1

Example, the table below shows bitwise OR logic between two random binary numbers.

Bit position	3	2	1	0
Binary value 1	1	0	0	1
Binary value 2	0	1	0	1
OR result	1	1	0	1

Bit position 1 is the only operation that has 0 in both bits, the remaining bits result in 1.

What are the differences between the BITAND, BITOR,BITXOR,BITRSHIFT, and BITLSHIFT functions?

Operation	Description	Example	Result
BITAND	Returns 1 only if both bits are 1	BITAND(5, 3)	1 (binary: 101 & 011 = 001)
BITOR	Returns 1 if either bit is 1	BITOR(5, 3)	7 (binary: 101 | 011 = 111)
BITXOR	Returns 1 if bits are different	BITXOR(5, 3)	6 (binary: 101 ^ 011 = 110)
BITRSHIFT	Shifts bits right (divides by 2^n)	BITRSHIFT(8, 2)	2 (binary: 1000 >> 2 = 0010)
BITLSHIFT	Shifts bits left (multiplies by 2^n)	BITLSHIFT(2, 2)	8 (binary: 0010 << 2 = 1000)

2. Syntax

BITOR(number1, number2)

3. Arguments

number1	Required. The first number.
number1	Required. The second number.

4. Example

The image above demonstrates the BITOR function in cell D3, the arguments are in cells B3 and B4 respectively.

Formula in cell D3:

Cells C3 and C4 shows the binary representation of the decimal numbers in cells B3 and B4. The BITOR function in cell D3 returns 13 from the decimal numbers 5 and 9.

The second example is demonstrated in cell D8:

The BITOR function in cell D8 returns 61 from decimal numbers 45 and 21.

The next sections explains how bit-wise OR logic works.

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5. How is the function calculated in detail?

Here are the steps to perform bit-wise OR logic:

1. Convert both decimal numbers to binary.
2. Perform bit-wise OR logic.
3. Convert binary output back to decimal again.

Example 1

Number 5 is 0000 0101 in binary and number 9 is 0000 1001. If at least one bit is 1 the returning digit is 1.

101 + 1101 = 1101. 1101 is the decimal number 13.

Example 2

Number 45 is 0010 1101 in binary and number 21 is 0001 0101. If at least one bit is 1 the returning digit is 1.

Bit position	7	6	5	4	3	2	1	0
Decimal number 45	0	0	1	0	1	1	0	1
Decimal number 21	0	0	0	1	0	1	0	1
OR result	0	0	1	1	1	1	0	1

The bitwise OR operation results in 0011 1101 which is decimal number 61.

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6. Function not working

The BITOR function returns a #NUM! error if

• argument number is 2^48 = 2.81475E+14 or larger. See row 4 in the image above.
• argument number is negative. See row 3 in the image above.

The BITOR function returns a #VALUE! error if the argument is a letter. See row 5 in the image above.

The BITAND function seems to work with boolean values TRUE and FALSE. See row 6 in the image above.

6.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

6.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference B3 converted to hard-coded value using the F9 key. The BITOR function requires positive numerical values which is not the case in this example. We have found what is wrong with the formula.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

6.3 Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

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7. How to perform bit-wise OR operations between binary numbers?

The following formula lets you perform bit-wise OR logic based on two binary numbers, the result is also a binary number. The image above shows binary numbers '0000 0101' and '00001001' in cells B3, and B4 respectively. They represent 5 and 9 in the decimal system shown in cells C3, and C4.

Formula:

Cells C3 and C4 shows the decimal representation of the specified binary numbers in cells B3 and B4, cells C3 and C4 are not needed. They are only shown for clarification.

Here is a quick break-down of the formula:

1. BIN2DEC(B3) and BIN2DEC(C3): Convert binary numbers to decimal numbers.
2. BITOR(BIN2DEC(B3), BIN2DEC(C3)): Perform bit-wise OR operation between decimal numbers.
3. DEC2BIN(BITOR(BIN2DEC(B3), BIN2DEC(C3)), 8): Convert the result shown in decimal back to binary.

Explaining formula

Step 1 - Convert binary number to decimal the system

The BIN2DEC function converts a binary number to the decimal number system.

Function syntax: BIN2DEC(number)

BIN2DEC(B3)

becomes

BIN2DEC("00000101")

and returns 5

Step 2 - Perform bitwise XOR operation

The BITOR function performs a bitwise 'OR' of two numbers.

Function syntax: BITOR(number1, number2)

BITOR(BIN2DEC(B3),BIN2DEC(C3))

becomes

BITOR(5,9)

and returns 13

Step 3 - Convert result to binary

The DEC2BIN function converts a decimal number to a binary number.

Function syntax: DEC2BIN(number, [places])

DEC2BIN(BITOR(BIN2DEC(B3),BIN2DEC(C3)),8)

beomes

DEC2BIN(13)

and returns

"00001101".

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8. Calculate combined user permissions

Suppose you have permissions for a document (Read = 4, Write = 2, Run = 1). What would be the combined number for these users:

• Tom : Read and run permissions
• Laura : Read, write, and run permissions
• Kim : Read, write, and run permissions

Formula in cell F5:

Here is a break-down of the formula:

1. BITOR(C5,D5): Perform bit-wise OR operation between Read and write permissions.
2. BITOR(BITOR(C5,D5),E5): Perform bit-wise OR operation between the result of Read, Write and the third "Run" permission.

Tom has 4 and 1 which returns 5. Laura has 4, 2, and 1 which returns 7. Kim has 4 which returns 4.

Useful resources

BITOR function - Microsoft support
Bitwise OR - wikipedia

'BITOR' function examples

The following article has a formula that contains the BITOR function.

Functions in 'Engineering' category

The BITOR function function is one of 42 functions in the 'Engineering' category.

Excel function categories

Excel categories

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