How to use the BITAND function

What is the BITAND function?

The BITAND function calculates a bitwise 'AND' of two decimal numbers. Note, it also returns a decimal number.

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?

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

What is an AND operation?

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

The following operations show that AND logic is the same as multiplying binary numbers:

0*0=0
1*0=0
0*1=0
1*1=1

Example, the table below shows bitwise AND 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
AND result	0	0	0	1

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

When is bit-wise AND logic useful?

1. Checking if a number is even or odd: To check if a number is even, we can use BITAND with 1. If the result is 0, the number is even. Example 1:
   • 6 (decimal) = 0110 (binary)
   • 1 (decimal) = 0001 (binary)
   • 6 BITAND 1 = 0110 AND 0001 = 0000 (Result is 0, so 6 is even)
   • Example 2:
   • 7 (decimal) = 0111 (binary)
   • 1 (decimal) = 0001 (binary)
   • 7 BITAND 1 = 0111 AND 0001 = 0001 (Result is 1, so 7 is odd)
2. Extracting specific bits from a number: Let's say we want to extract the 3rd and 4th bits from a byte. Example:
   • Original number: 170 (decimal) = 10101010 (binary)
   • Mask: 12 (decimal) = 00001100 (binary)
   • 170 BITAND 12= 10101010 AND 00001100 = 00001000 (8 in decimal)
3. Implementing simple permissions systems: We can use BITAND to check if a user has specific permissions. Example:
   • User permissions: 5 (decimal) = 0101 (binary) (Read and Run)
   • Required permission: 4 (decimal) = 0100 (binary) (Write)
   • 5 BITAND 4 = 0101 AND 0100 = 0100
   • Since the result is non-zero, the user has the required permission.
4. Clearing specific bits: To clear (set to 0) specific bits in a number, we can use BITAND with a mask. Example:
   • Original number: 255 (decimal) = 11111111 (binary)
   • Mask: 247 (decimal) = 11110111 (binary) (to clear the 4th bit)
   • 255 BITAND 247 = 11111111 AND 11110111 = 11110111 (247 in decimal)

2. Syntax

BITAND(number1, number2)

number1	Required. The first number.
number2	Required. The second number.

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3. Example

The image above shows the BITAND function cell D3, it has two arguments number 1 and number2 which are specified in cells B3 and B4. Their binary representation are in cells C8 and C9 respectively.

Formula in cell D3:

The formula in cell D3 returns 1 which is the decimal representation of binary AND-logic of 5 and 9. It performs AND logic for each bit between the two decimal numbers and the binary result is converted into a decimal number which in this case is 1.

The next formula in cell D8 performs a bit-wise AND-logic between decimal numbers 45 and 21 which are located in cells B8 and B9 respectively. The result is shown in cell D8 which contains 5. The binary AND-logic is shown in cells C8 and C9 and the binary result is displayed in cell C10.

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4. How is the function calculated in detail?

Here are the steps to perform bitwise AND logic:

1. Convert both decimal numbers to binary.
2. Perform bitwise AND logic.
3. Convert binary output back to decimal again.

Example 1,

Decimal number 5 is 0000 0101 in binary and decimal number 9 is 0000 1001 in binary.

With AND logic bitwise the result is 0000 0001 which is number 1.

Example 2,

Decimal number 45 is 0010 1101 in binary and decimal number 21 is 0001 0101 in binary.

Bit position	7	6	5	4	3	2	1	0
Binary value 1	0	0	1	0	1	1	0	1
Binary value 2	0	0	0	1	0	1	0	1
AND result	0	0	0	0	0	1	0	1

The bitwise AND logic results in 0000 0101 which is the decimal number 5.

5. Function not working

The BITAND 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 BITAND 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.

5.1 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.

5.2 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 BITAND function requires numerical values larger than or equal to 0 (zero) in the first argument 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

5.3 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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6. How to perform bitwise AND operations between binary numbers?

The following example demonstrates a formula that lets you calculate bit-wise AND logic between two binary numbers, the result is also binary.

Formula in cell D3:

Here is a breakdown of how it works:

• BIN2DEC(B3) and BIN2DEC(C3) convert the binary numbers in cells B3 and C3 to decimal numbers.
• BITAND(BIN2DEC(B3),BIN2DEC(C3)): BITAND performs a bitwise AND operation between the two decimal numbers. This operation compares each bit of the first number to the corresponding bit of the second number. If both bits are 1, the corresponding result bit is set to 1. Otherwise, the corresponding result bit is set to 0.
• DEC2BIN(BITAND(BIN2DEC(B3),BIN2DEC(C3))): DEC2BIN converts the result of the bitwise AND operation back to a binary number.

For example, if B3 contains the binary number 0000 0101 and C3 contains the binary number 0110 0101, the formula would work as follows:

• BIN2DEC(B3) converts 0000 0101 to the decimal number 5.
• BIN2DEC(C3) converts 0110 0101 to the decimal number 101.
• BITAND(5, 101) performs the bitwise AND operation, resulting in the decimal number 5.
• DEC2BIN(5) converts the result back to the binary number 0000 0101.
  The final result of the formula is 0000 0101.

Explaining formula

Step 1 - Convert binary to decimal

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 AND operation

The BITAND function calculates a bitwise 'AND' of two numbers.

Function syntax: BITAND(number1, number2)

BITAND(BIN2DEC(B3),BIN2DEC(C3))

becomes

BITAND(5,101)

and returns 5.

Step 3 - Convert result to back to binary

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

Function syntax: DEC2BIN(number, [places])

DEC2BIN(BITAND(BIN2DEC(B3),BIN2DEC(C3)))

becomes

DEC2BIN(5)

and returns "00000101".

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Useful resources

BITAND function - Microsoft
Bitwise operation - Wikipedia

'BITAND' function examples

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

Functions in 'Engineering' category

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

Excel function categories

Excel categories

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