## How to use the BITLSHIFT function

##### What is the BITLSHIFT function?

The BITLSHIFT function calculates a decimal number whose binary representation is shifted left by a specified 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 **b**inary dig**it **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 left?

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

The result of shifting bits left is the same as multiplying the original value by a power of two. For example, shift decimal value 10 left by one position we get 20 which is 10 times 2. If we shift it left by two positions we get 40 which is 10 * 2 * 2

Decimal value 10 is 1010 in the binary system. Add a zero to the right side and we get 10100 which is 20 in the decimal system.

##### Why shift bits left?

Bits shifted left can be used for performing arithmetic operations, manipulating bits, or encoding data. However, the BITLSHIFT function works only for positive decimal numbers. It is therefore not possible to change the significant bit when shifting left.

##### What are significant bits?

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.

### Table of Contents

## 1. BITLSHIFT Function Syntax

BITLSHIFT(*number*,Â *shift_amount*)

## 2. BITLSHIFT 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. BITLSHIFT function example

The image above demonstrates a formula in cell D3 that shifts bits left based on a decimal number specified in cell B3, the number of positions shifted left 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 right side and you get 1010 binary which is number 10 in the decimal system.

*Example 2,*

Cell B8 contains decimal number 41 which is 0010 1001 in the binary system, cell C8 contains 1 which means that the binary digits are shifted left by one position. Add a 0 (zero) to the right side and you get 0101 0010 in binary which is number 82 in the decimal system.

## 4. How is the BITLSHIFT function calculated in detail?

The table below shows how bits are shifted left using the BITLSHIFT function by one position.

Bit position |
3 |
2 |
1 |
0 |

Binary value 5 |
0 | 1 | 0 | 1 |

BITLSHIFT result |
1 | 0 | 1 | 0 |

Simply add a 0 (zero) to the right side of the binary number to shift bits one step, this applies to multiple steps as well.

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

Decimal number 5 is 0101 in the binary system, shifting bits 3 positions results in this binary number: 0010 1000 which is equal to decimal number 40.

## 5. BITLSHIFT function not working

The BITLSHIFT 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. - argument
*number*is smaller than 0 (zero).

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

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

## 6. How to shift bits using binary numbers?

The BITLSHIFT function needs a decimal number to be able to shift the binary representation left 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 left

The BITLSHIFT function calculates a number whose binary representation is shifted left by a specified number of bits.

Function syntax: BITLSHIFT(number,Â shift_amount)

BITLSHIFT(BIN2DEC(B3),C3)

becomes

BITLSHIFT(5,1)

and returns 10

#### Step 3 - Convert result to binary

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

Function syntax: DEC2BIN(number, [places])

DEC2BIN(BITLSHIFT(BIN2DEC(B3),C3))

becomes

DEC2BIN(10)

and returns

"1010".

### Useful resources

BITLSHIFT function - Microsoft support

Bit shifts - Wikipedia

### Functions in 'Engineering' category

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

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