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.

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 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 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).

1. BITAND function Syntax

BITAND(number1, number2)

2. BITAND function Arguments

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

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3. BITAND function 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.

Formula in cell B3:

The formula in cell B3 performs AND logic for each bit between decimal numbers and returns a decimal number.

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4. How is the BITAND 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. BITAND 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.

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

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

Formula:

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

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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