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.
Table of Contents
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 | 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 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 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 bit-wise 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 |
What is the difference between XOR and OR operations in binary?
The XOR (exclusive OR) and OR operations are both binary operations, meaning they operate on pairs of bits, but they have different rules for determining their output.
OR Operation
The OR operation outputs 1 if at least one of the input bits is 1. Otherwise, it outputs 0.
| 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 |
XOR Operation
The XOR (exclusive OR) operation outputs 1 only if the input bits are different. If both bits are the same, both 0 or both 1, it outputs 0.
| 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 |
This distinction makes XOR useful in applications like error detection and encryption, where the ability to distinguish differences is crucial.
2. Syntax
BITXOR(number1, number2)
3. Arguments
| number1 | Required. A number greater than 0 (zero). |
| number2 | Required. A number greater than 0 (zero). |
4. 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.
5. 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".
6. 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.
7. 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. The image above shows two binary numbers in cells B3 and B4, they are: 0000 0101 and 0000 1001 which represent 5 and 9 in decimal (base 10) respectively. The BITXOR function requires decimal numbers as input values, you can't use binary numbers.
Formula in cell D3:
The formula in cell D3 converts the binary numbers specified in cells B3 and B4 to decimal numbers, then the BBITXOR function performs XOR logic between the decimal numbers.
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.
The output value from the BITXOR function is also a decimal number, DEC2BIN function converts the output back to binary again. For example, a bit-wise XOR between binary numbers 0000 0101 and 0000 1010 is equal to 0000 1100 in binary which represents 12 in decimal.
The second example displayed in cells B8 and B9 contain binary numbers 0010 1101 and 0001 0101 respectively which represent 45 and 21 in decimal. A bit-wise XOR operation between these binary numbers is equal to 0011 1000 which represents 56 in decimal.
Here is a quick break-down of the formula in cell D3:
- BIN2DEC(B3): Converts binary numbers to decimal numbers.
- BITXOR(BIN2DEC(B3),BIN2DEC(B4)): Performs a bit-wise XOR between two decimal numbers and the result is a decimal number.
- DEC2BIN(BITXOR(BIN2DEC(B3),BIN2DEC(B4)),8): Converts the decimal number 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 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
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Functions in 'Engineering' category
The BITXOR function function is one of 42 functions in the 'Engineering' category.
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