About Arithmetic Operators

Article
12/01/2022

SHORT DESCRIPTION

Describes the operators that perform arithmetic in PowerShell.

LONG DESCRIPTION

Arithmetic operators calculate numeric values. You can use one or more arithmetic operators to add, subtract, multiply, and divide values, and to calculate the remainder (modulus) of a division operation.

In addition, the addition operator (+) and multiplication operator (*) also operate on strings, arrays, and hash tables. The addition operator concatenates the input. The multiplication operator returns multiple copies of the input. You can even mix object types in an arithmetic statement. The method that is used to evaluate the statement is determined by the type of the leftmost object in the expression.

Beginning in PowerShell 2.0, all arithmetic operators work on 64-bit numbers.

Beginning in PowerShell 3.0, the -shr (shift-right) and -shl (shift-left) are added to support bitwise arithmetic in PowerShell.

PowerShell supports the following arithmetic operators:

Operator	Description	Example
+	Adds integers; concatenates	`6 + 2`
	strings, arrays, and hash tables.	`"file" + "name"`
		`@(1, "one") + @(2.0, "two")`
		`@{"one" = 1} + @{"two" = 2}`
-	Subtracts one value from another	`6 - 2`
	value
-	Makes a number a negative number	`-6`
		`(Get-Date).AddDays(-1)`
*	Multiply numbers or copy strings	`6 * 2`
	and arrays the specified number	`@("!") * 4`
	of times.	`"!" * 3`
/	Divides two values.	`6 / 2`
%	Modulus - returns the remainder of	`7 % 2`
	a division operation.
-band	Bitwise AND	`5 -band 3`
-bnot	Bitwise NOT	`-bnot 5`
-bor	Bitwise OR	`5 -bor 0x03`
-bxor	Bitwise XOR	`5 -bxor 3`
-shl	Shifts bits to the left the	`102 -shl 2`
	specified number of times
-shr	Shifts bits to the right	`102 -shr 2`

The bitwise operators only work on integer types.

OPERATOR PRECEDENCE

PowerShell processes arithmetic operators in the following order:

Precedence	Operator	Description
1	`()`	Parentheses
2	`-`	For a negative number or unary operator
3	`*`, `/`, `%`	For multiplication and division
4	`+`, `-`	For addition and subtraction

PowerShell processes the expressions from left to right according to the precedence rules. The following examples show the effect of the precedence rules:

Expression	Result
`3+6/3*4`	`11`
`3+6/(3*4)`	`3.5`
`(3+6)/3*4`	`12`

The order in which PowerShell evaluates expressions might differ from other programming and scripting languages that you have used. The following example shows a complicated assignment statement.

$a = 0
$b = @(1,2)
$c = @(-1,-2)

$b[$a] = $c[$a++]

In this example, the expression $a++ is evaluated before $b[$a]. Evaluating $a++ changes the value of $a after it is used in the statement $c[$a++]; but, before it is used in $b[$a]. The variable $a in $b[$a] equals 1, not 0; so, the statement assigns a value to $b[1], not $b[0].

The above code is equivalent to:

$a = 0
$b = @(1,2)
$c = @(-1,-2)

$tmp = $c[$a]
$a = $a + 1
$b[$a] = $tmp

DIVISION AND ROUNDING

When the quotient of a division operation is an integer, PowerShell rounds the value to the nearest integer. When the value is .5, it rounds to the nearest even integer.

The following example shows the effect of rounding to the nearest even integer.

Expression	Result
`[int]( 5 / 2 )`	`2`
`[int]( 7 / 2 )`	`4`

Notice how 5/2 = 2.5 gets rounded to 2. But, 7/2 = 3.5 gets rounded to 4.

ADDING AND MULTIPLYING NON-NUMERIC TYPES

You can add numbers, strings, arrays, and hash tables. And, you can multiply numbers, strings, and arrays. However, you cannot multiply hash tables.

When you add strings, arrays, or hash tables, the elements are concatenated. When you concatenate collections, such as arrays or hash tables, a new object is created that contains the objects from both collections. If you try to concatenate hash tables that have the same key, the operation fails.

For example, the following commands create two arrays and then add them:

$a = 1,2,3
$b = "A","B","C"
$a + $b

1
2
3
A
B
C

You can also perform arithmetic operations on objects of different types. The operation that PowerShell performs is determined by the Microsoft .NET Framework type of the leftmost object in the operation. PowerShell tries to convert all the objects in the operation to the .NET Framework type of the first object. If it succeeds in converting the objects, it performs the operation appropriate to the .NET Framework type of the first object. If it fails to convert any of the objects, the operation fails.

The following examples demonstrate the use of the addition and multiplication operators; in operations that include different object types. Assume $array = 1,2,3:

Expression	Result
`"file" + 16`	`file16`
`$array + 16`	`1`,`2`,`3`,`16`
`$array + "file"`	`1`,`2`,`3`,`file`
`$array * 2`	`1`,`2`,`3`,`1`,`2`,`3`
`"file" * 3`	`filefilefile`

Because the method that is used to evaluate statements is determined by the leftmost object, addition and multiplication in PowerShell are not strictly commutative. For example, (a + b) does not always equal (b + a), and (ab) does not always equal (ba).

The following examples demonstrate this principle:

Expression	Result
`"file" + 16`	`file16`
`16 + "file"`	`Cannot convert value "file" to type "System.Int32".`
	`Error: "Input string was not in a correct format."`
	`At line:1 char:1`
	+ 16 + "file"`

Hash tables are a slightly different case. You can add hash tables to another hash table, as long as, the added hash tables don't have duplicate keys.

The following example show how to add hash tables to each other.

$hash1 = @{a=1; b=2; c=3}
$hash2 = @{c1="Server01"; c2="Server02"}
$hash1 + $hash2

Name                           Value
----                           -----
c2                             Server02
a                              1
b                              2
c1                             Server01
c                              3

The following example throws an error because one of the keys is duplicated in both hash tables.

$hash1 = @{a=1; b=2; c=3}
$hash2 = @{c1="Server01"; c="Server02"}
$hash1 + $hash2

Item has already been added. Key in dictionary: 'c'  Key being added: 'c'
At line:3 char:1
+ $hash1 + $hash2
+ ~~~~~~~~~~~~~~~
    + CategoryInfo          : OperationStopped: (:) [], ArgumentException
    + FullyQualifiedErrorId : System.ArgumentException

Also, you can add a hash table to an array; and, the entire hash table becomes an item in the array.

$array1 = @(0, "Hello World", [datetime]::Now)
$hash1 = @{a=1; b=2}
$array2 = $array1 + $hash1
$array2

0
Hello World

Monday, June 12, 2017 3:05:46 PM

Key   : a
Value : 1
Name  : a

Key   : b
Value : 2
Name  : b

However, you cannot add any other type to a hash table.

$hash1 + 2

A hash table can only be added to another hash table.
At line:3 char:1
+ $hash1 + 2

Although the addition operators are very useful, use the assignment operators to add elements to hash tables and arrays. For more information see about_assignment_operators. The following examples use the += assignment operator to add items to an array:

$array = @()
(0..9).foreach{ $array += $_ }
$array

0
1
2

TYPE CONVERSION TO ACCOMMODATE RESULT

PowerShell automatically selects the .NET Framework numeric type that best expresses the result without losing precision. For example:

2 + 3.1

(2). GetType().FullName
(2 + 3.1).GetType().FullName

5.1
System.Int32
System.Double

If the result of an operation is too large for the type, the type of the result is widened to accommodate the result, as in the following example:

(512MB).GetType().FullName
(512MB * 512MB).GetType().FullName

System.Int32
System.Double

The type of the result will not necessarily be the same as one of the operands. In the following example, the negative value cannot be cast to an unsigned integer, and the unsigned integer is too large to be cast to Int32:

([int32]::minvalue + [uint32]::maxvalue).gettype().fullname

System.Int64

In this example, Int64 can accommodate both types.

The System.Decimal type is an exception. If either operand has the Decimal type, the result will be of the Decimal type. If the result is too large for the Decimal type, it will not be cast to Double. Instead, an error results.

Expression	Result
`[Decimal]::maxvalue`	`79228162514264337593543950335`
`[Decimal]::maxvalue + 1`	`Value was either too large or too small for a`
	`Decimal.`

ARITHMETIC OPERATORS AND VARIABLES

You can also use arithmetic operators with variables. The operators act on the values of the variables. The following examples demonstrate the use of arithmetic operators with variables:

Expression	Result
`$intA = 6` `$intB = 4` `$intA + $intB`	`10`
`$a = "Power"` `$b = "Shell"` `$a + $b`	`PowerShell`

ARITHMETIC OPERATORS AND COMMANDS

Typically, you use the arithmetic operators in expressions with numbers, strings, and arrays. However, you can also use arithmetic operators with the objects that commands return and with the properties of those objects.

The following examples show how to use the arithmetic operators in expressions with PowerShell commands:

(get-date) + (new-timespan -day 1)

The parenthesis operator forces the evaluation of the get-date cmdlet and the evaluation of the new-timespan -day 1 cmdlet expression, in that order. Both results are then added using the + operator.

Get-Process | Where-Object { ($_.ws * 2) -gt 50mb }

Handles  NPM(K)    PM(K)      WS(K) VM(M)   CPU(s)     Id ProcessName
-------  ------    -----      ----- -----   ------     -- -----------
   1896      39    50968      30620   264 1,572.55   1104 explorer
  12802      78   188468      81032   753 3,676.39   5676 OUTLOOK
    660       9    36168      26956   143    12.20    988 PowerShell
    561      14     6592      28144   110 1,010.09    496 services
   3476      80    34664      26092   234 ...45.69    876 svchost
    967      30    58804      59496   416   930.97   2508 WINWORD

In the above expression, each process working space ($_.ws) is multiplied by 2; and, the result, compared against 50mb to see if it is greater than that.

Bitwise Operators

PowerShell supports the standard bitwise operators, including bitwise-AND (-bAnd), the inclusive and exclusive bitwise-OR operators (-bOr and -bXor), and bitwise-NOT (-bNot).

Beginning in PowerShell 2.0, all bitwise operators work with 64-bit integers.

Beginning in PowerShell 3.0, the -shr (shift-right) and -shl (shift-left) are introduced to support bitwise arithmetic in PowerShell.

PowerShell supports the following bitwise operators.

Operator	Description	Expression	Result
`-band`	Bitwise AND	`10 -band 3`	2
`-bor`	Bitwise OR (inclusive)	`10 -bor 3`	11
`-bxor`	Bitwise OR (exclusive)	`10 -bxor 3`	9
`-bnot`	Bitwise NOT	`-bNot 10`	-11
`-shl`	Shift-left	`102 -shl 2`	408
`-shr`	Shift-right	`102 -shr 1`	51

Bitwise operators act on the binary format of a value. For example, the bit structure for the number 10 is 00001010 (based on 1 byte), and the bit structure for the number 3 is 00000011. When you use a bitwise operator to compare 10 to 3, the individual bits in each byte are compared.

In a bitwise AND operation, the resulting bit is set to 1 only when both input bits are 1.

1010      (10)
0011      ( 3)
--------------  bAND
0010      ( 2)

In a bitwise OR (inclusive) operation, the resulting bit is set to 1 when either or both input bits are 1. The resulting bit is set to 0 only when both input bits are set to 0.

1010      (10)
0011      ( 3)
--------------  bOR (inclusive)
1011      (11)

In a bitwise OR (exclusive) operation, the resulting bit is set to 1 only when one input bit is 1.

1010      (10)
0011      ( 3)
--------------  bXOR (exclusive)
1001      ( 9)

The bitwise NOT operator is a unary operator that produces the binary complement of the value. A bit of 1 is set to 0 and a bit of 0 is set to 1.

For example, the binary complement of 0 is -1, the maximum unsigned integer (0xffffffff), and the binary complement of -1 is 0.

PS C:\> -bNot 10
-11

0000 0000 0000 1010  (10)
------------------------- bNOT
1111 1111 1111 0101  (-11, xfffffff5)

In a bitwise shift-left operation, all bits are moved "n" places to the left, where "n" is the value of the right operand. A zero is inserted in the ones place.

When the left operand is an Integer (32-bit) value, the lower 5 bits of the right operand determine how many bits of the left operand are shifted.

When the left operand is a Long (64-bit) value, the lower 6 bits of the right operand determine how many bits of the left operand are shifted.

Expression	Result	Binary Result
`21 -shl 0`	21	0001 0101
`21 -shl 1`	42	0010 1010
`21 -shl 2`	84	0101 0100

In a bitwise shift-right operation, all bits are moved "n" places to the right, where "n" is specified by the right operand. The shift-right operator (-shr) inserts a zero in the left-most place when shifting a positive or unsigned value to the right.