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.

3. 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.

Back to top

4. How is the BITOR 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.

Back to top

5. BITOR 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.

Back to top

6. 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".

Back to top

Back to top

7. 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

Leave a Comment