How to use the BITXOR function
What is the BITXOR function?
The BITXOR function calculates a decimal number that is a result of a bitwise comparison "XOR" of two decimal numbers, XOR stands for Exclusive OR.
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 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
What is bitwise?
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 XOR operations.
What is an XOR operation?
The BITXOR function performs XOR logic bit by bit on the numbers based on their binary representation. XOR is an abbreviation for "Exclusive OR" meaning if both digits at each position are not equal, 1 is returned for that position. If they are equal 0 (zero) is returned.
The following operations show how XOR logic work:
0+0=0
1+0=1
0+1=1
1+1=0
Example, the table below shows bitwise XOR 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 |
| XOR result | 1 | 1 | 0 | 0 |
Table of Contents
1. BITXOR Function Syntax
BITXOR(number1, number2)
2. BITXOR Function Arguments
| number1 | Required. A number greater than 0 (zero). |
| number2 | Required. A number greater than 0 (zero). |
3. BITXOR Function example
The image above demonstrates a formula in cell D3 that performs exclusive OR between two decimal numbers specified in cells B3 and B4. The decimal numbers are automatically converted in to binary digits and then the BITXOR function performs an exclusive OR operation. Lastly, the binary result is then converted back in to a decimal number.
Formula in cell D3:
The image above shows numbers 5 and 9 in cells B3 and B4 respectively. The BITXOR function converts the decimal numbers to binary numbers 0000 0101 and 0000 1001, the exclusive OR is 0000 1100 which represents 12 in the decimal system shown in cell D3.
4. How is the BITXOR function calculated in detail?
Here are the steps to perform bitwise XOR logic:
- Convert both decimal numbers to binary.
- Perform bitwise XOR logic, here are the rules:
0+0=0
1+0=1
0+1=1
1+1=0 - Convert binary output back to decimal again.
Example
5 is 00000101 binary and 9 is 00001001. See picture below on how to do a bitwise "XOR".
5. BITXOR function not working
The BITXOR 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. How to perform bitwise XOR operations between binary numbers?
The following formula lets you perform bitwise XOR logic based on binary numbers, the result is also a binary number.
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.
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 OR operation
The BITXOR function calculates a decimal number that is a result of a bitwise comparison "XOR" of two numbers.
Function syntax: BITXOR(number1, number2)
BITXOR(BIN2DEC(B3),BIN2DEC(C3))
becomes
BITXOR(5,9)
and returns 12
Step 3 - Convert result to binary
The DEC2BIN function converts a decimal number to a binary number.
Function syntax: DEC2BIN(number, [places])
DEC2BIN(BITXOR(BIN2DEC(B3),BIN2DEC(C3)),8)
beomes
DEC2BIN(12)
and returns
"00001100".
Useful resources
BITXOR function - Microsoft support
Bitwise XOR - wikipedia
'BITXOR' function examples
The following article has a formula that contains the BITXOR function.
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Functions in 'Engineering' category
The BITXOR function function is one of many functions in the 'Engineering' category.
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