What is the BITRSHIFT function?

The BITRSHIFT function calculates a number based on the decimal system whose binary representation is shifted right by a given number of bits.

What is the binary system?

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 are bits?

A bit is a binary digit meaning the single digit in a binary number. Binary numbers are often split into four bits, four bits represents decimal numbers from 0 to 15 or hexadecimal numbers from 0 to F. For example, binary number 0010 has four bits.

What is bits shifted right?

Each bit is moved one position to the right, the easiest way to do this is to add a zero on the left side of the binary number and remove the last digit on the right side to shift bits one position.

Why shift bits right?

Bits shifted left can be used for performing arithmetic operations, manipulating bits, or encoding data. The BITRSHIFT function works only for positive numbers in the decimal system, there is no risk of changing the significant bit when shifting right.

What is the significant bit?

The significant bit or sign bit indicates whether a binary number is positive or negative, if the bit is 0 the number is positive, if the bit is 1, the number is negative.

What is a magnitude bit?

The remaining bits are magnitude bits which represents the absolute value of the number. An absolute number is a number without the sign.

 

1. BITRSHIFT Function Syntax

BITRSHIFT(number, shift_amount)

2. BITRSHIFT Function Arguments

number	Required. The number you want to shift. Must be 0 (zero) or greater than 0 (zero).
shift_amount	Required. How many zeros you want to add to the right side. This number can be negative as well,

3. BITRSHIFT function example

The image above demonstrates a formula in cell D3 that shifts bits right based on a decimal number specified in cell B3, the number of positions shifted right is specified in cell C3.

Formula in cell D3:

Example 1,

Cell B3 contains decimal number 5 which is 0101 in the binary system. Add a 0 (zero) to the left side and remove the last bit on the right side and you get 0010 binary which is number 2 in the decimal system.

Example 2,

Cell B8 contains decimal number 41 which is 0010 1001 in the binary system, cell C8 contains 2 which means that the binary digits are shifted right by two positions. Add two 0's (zeros) to the left side and remove two bits on the right side and you get 0000 1010 in binary which is number 10 in the decimal system.

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4. How is the BITRSHIFT function calculated in detail?

The table below shows how bits are shifted right using the BITRSHIFT function by one position.

Bit position	3	2	1	0
Binary value 5	0	1	0	1
BITRSHIFT result	0	0	1	0

To shift bits one position to the right add a 0 (zero) to the left side of the binary number and remove the last bit on the right side.

Example 2, to shift bits two steps right add the same amount of 0's (zeros) to the left side of the binary number, in this example two 0's (zeros).

Decimal number 5 is 0101 in the binary system, shifting bits 2 positions results in this binary number: 0001 which is equal to decimal number 1.

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5. BITRSHIFT function not working

The BITRSHIFT function returns a #NUM! error if

• argument number is 2^48 = 2.81475E+14 or larger. See row 3 in the image above.
• argument number is negative.
• argument number is smaller than 0 (zero).
• argument shift_amount is larger than 53

The BITRSHIFT function returns a #VALUE! error if either of the argument is a letter. See row 5 in the image above.

The BITRSHIFT function seems to work with boolean values TRUE and FALSE. See row 6 in the image above.

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6. How to shift bits with binary numbers?

The BITRSHIFT function needs a decimal number to be able to shift the binary representation right and the return the decimal representation of the shifted bits.

The following formula lets you shift binary numbers based on a given number of shifts, the result is also a binary number.

Formula in cell D3:

The formula is limited by the BIN2DEC and DEC2BIN functions, they can only handle decimal numbers from -512 to 511.

The following formula works for larger numbers:

However, this may create a new problem with the sign bit that shows if a binary number is positive or negative.

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 - Shift bits to the right

The BITRSHIFT function calculates the number where the binary equivalent is shifted right by a specified number of bits and then converted back to a number.

Function syntax: BITRSHIFT(number, shift_amount)

BITRSHIFT(BIN2DEC(B3),C3)

becomes

BITRSHIFT(5,1)

and returns 2

Step 3 - Convert result to binary

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

Function syntax: DEC2BIN(number, [places])

DEC2BIN(BITRSHIFT(BIN2DEC(B3),C3))

becomes

DEC2BIN(2)

and returns

"0010".

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Useful resources

BITRSHIFT function - Microsoft support
Bit shifts - Wikipedia

Functions in 'Engineering' category

The BITRSHIFT function function is one of many functions in the 'Engineering' category.

Excel function categories

Excel categories

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