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The Boolean palette provides constants and functions that can be performed on [[Boolean]], [[Numeric]] and [[Fixed-point]] values.
The Boolean palette provides constants and functions that can be performed on [[Boolean]], [[Numeric]] and [[Fixed-point]] values.


== [[File:Andfunct.png|Logical And]] Logical And ==
== Functions ==
 
Accepts two Boolean or [[Numeric|numeric]] inputs.
 
'''Boolean''': If provided Boolean values, returns [[File:BooleanTrue2010.png|border|True]] if both inputs are [[File:BooleanTrue2010.png|border|True]], otherwise returns [[File:BooleanFalse2010.png|border|False]].
 
{| class="wikitable"
! x
! y
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|}
 
'''Numeric''': If provided [[Numeric|numeric]] values, performs a bit-wise AND operation.
 
{| class="wikitable"
!
! Binary
! Decimal
|-
! x
| <code>10101010</code>
| style="text-align: center;" | 170
|-
! y
| <code>11110000</code>
| style="text-align: center;" | 240
|-
! output
| <code>10100000</code>
| style="text-align: center;" | 160
|}
 
== [[File:Orfunct.png|Logical Or]] Logical Or ==
 
Accepts two Boolean or [[Numeric|numeric]] inputs.
 
'''Boolean''': If provided Boolean values, returns [[File:BooleanTrue2010.png|border|True]] if any input is [[File:BooleanTrue2010.png|border|True]], otherwise returns [[File:BooleanFalse2010.png|border|False]].
 
{| class="wikitable"
! x
! y
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|}
 
'''Numeric''': If provided [[Numeric|numeric]] values, performs a bit-wise OR operation.
 
{| class="wikitable"
!
! Binary
! Decimal
|-
! x
| <code>10101010</code>
| style="text-align: center;" | 170
|-
! y
| <code>11110000</code>
| style="text-align: center;" | 240
|-
! output
| <code>11111010</code>
| style="text-align: center;" | 250
|}
 
== [[File:Xclusvor.png|Exclusive Or]] Exclusive Or ==
 
Accepts two Boolean or [[Numeric|numeric]] inputs.
 
'''Boolean''': If provided Boolean values, returns [[File:BooleanTrue2010.png|border|True]] if any input is [[File:BooleanTrue2010.png|border|True]] exclusively, otherwise returns [[File:BooleanFalse2010.png|border|False]].


{| class="wikitable"
{| class="wikitable"
! x
| [[File:Andfunct.png|Logical And]]
! y
| [[And function|Logical And]]
! output
|-
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:Orfunct.png|Logical Or]]
| [[File:BooleanFalse2010.png|border|False]]
| [[Or function|Logical Or]]
| [[File:BooleanFalse2010.png|border|False]]
|-
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:Xclusvor.png|Exclusive Or]]
| [[File:BooleanTrue2010.png|border|True]]
| [[Exclusive Or function|Exclusive Or]]
| [[File:BooleanTrue2010.png|border|True]]
|-
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:Notfunct.png|Not]]
| [[File:BooleanFalse2010.png|border|False]]
| [[Not function|Not]]
| [[File:BooleanTrue2010.png|border|True]]
|-
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:Comparit.png|Compound Arithmetic]]
| [[File:BooleanTrue2010.png|border|True]]
| [[Compound Arithmetic function|Compound Arithmetic]]
| [[File:BooleanFalse2010.png|border|False]]
|}
 
'''Numeric''': If provided [[Numeric|numeric]] values, performs a bit-wise XOR operation.
 
{| class="wikitable"
!
! Binary
! Decimal
|-
|-
! x
| [[File:Notandfn.png|Not And]]
| <code>10101010</code>
| [[Not And function|Not And]]
| style="text-align: center;" | 170
|-
|-
! y
| [[File:Notorfun.png|Not Or]]
| <code>11110000</code>
| [[Not Or function|Not Or]]
| style="text-align: center;" | 240
|-
|-
! output
| [[File:Notxclor.png|Not Exclusive Or]]
| <code>01011010</code>
| [[Not Exclusive Or function|Not Exclusive Or]]
| style="text-align: center;" | 90
|}
 
== [[File:Notfunct.png|Not]] Not ==
 
Returns the inverted value of an Boolean or [[Numeric|numeric]] input.
 
'''Boolean''':
 
{| class="wikitable"
! x
! output
|-
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:Implies.png|Implies]]
| [[File:BooleanTrue2010.png|border|True]]
| [[Implies function|Implies]]
|-
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:Andarray.png|And Array Elements]]
| [[File:BooleanFalse2010.png|border|False]]
| [[And Array Elements function|And Array Elements]]
|}
 
'''Numeric:'''
 
{| class="wikitable"
!
! Binary
! Decimal
|-
|-
! x
| [[File:Orarray.png|Or Array Elements]]
| <code>10101010</code>
| [[Or Array Elements function|Or Array Elements]]
| style="text-align: center;" | 170
|-
|-
! output
| [[File:Numtoboo.png|Num to Array]]
| <code>01010101</code>
| [[Num to Array function|Num to Array]]
| style="text-align: center;" | -171
|}
 
== [[File:Comparit.png|Compound Arithmetic]] Compound Arithmetic ==
 
[[File:CompoundArithmeticChangeMode.png|thumb|Change mode on the Compound Arithmetic function]]
 
Performs various logical and arithmetic operations on Boolean and numeric values for a dynamic amount of inputs.
 
'''Available operations''':
 
* Add
* Multiply
* AND (see [[#Logical_And|Logical And]])
* OR (see [[#Logical_Or|Logical Or]])
* XOR (see [[#Exclusive_Or|Exclusive Or]])
 
This function is especially useful when doing logical and arithmetic operations on more than two input values.
 
'''Invert input and output''':
 
The Compound Arithmetic function allows to invert any of the inputs as well as the output selectively.
 
[[File:CompoundArithmeticInvertInput.png|frameless|border|Invert input on the Compound Arithmetic function]]
 
<br clear="all">
== [[File:Notandfn.png|Not And]] Not And ==
 
This is the same as [[#Logical_And|Logical And]] but the output is inverted.
 
'''Boolean''':
 
{| class="wikitable"
! x
! y
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|-
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:Bootonum.png|Array to Num]]
| [[File:BooleanFalse2010.png|border|False]]
| [[Array to Num function|Array to Num]]
| [[File:BooleanTrue2010.png|border|True]]
|-
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:Bootoone.png|Bool to (0,1)]]
| [[File:BooleanTrue2010.png|border|True]]
| [[Bool to (0,1) function|Bool to (0,1)]]
| [[File:BooleanFalse2010.png|border|False]]
|}
|}


'''Numeric'''
== Constants ==


{| class="wikitable"
{| class="wikitable"
!
| [[File:BooleanTrue2010.png|True Constant]]
! Binary
| [[True constant|True Constant]]
! Decimal
|-
! x
| <code>10101010</code>
| style="text-align: center;" | 170
|-
! y
| <code>11110000</code>
| style="text-align: center;" | 240
|-
|-
! output
| [[File:BooleanFalse2010.png|False Constant]]
| <code>01011111</code>
| [[False constant|False Constant]]
| style="text-align: center;" | 95
|}
|}
== [[File:Notorfun.png|Not Or]] Not Or ==
This is the same as [[#Logical_Or|Logical Or]] but the output is inverted.
'''Boolean''':
{| class="wikitable"
! x
! y
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
|}
'''Numeric''':
{| class="wikitable"
!
! Binary
! Decimal
|-
! x
| <code>10101010</code>
| style="text-align: center;" | 170
|-
! y
| <code>11110000</code>
| style="text-align: center;" | 240
|-
! output
| <code>00000101</code>
| style="text-align: center;" | 5
|}
== [[File:Notxclor.png|Not Exclusive Or]] Not Exclusive Or ==
This is the same as [[#Exclusive_Or|Exclusive Or]] but with inverted output.
'''Boolean''':
{| class="wikitable"
! x
! y
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|}
'''Numeric''':
{| class="wikitable"
!
! Binary
! Decimal
|-
! x
| <code>10101010</code>
| style="text-align: center;" | 170
|-
! y
| <code>11110000</code>
| style="text-align: center;" | 240
|-
! output
| <code>10100101</code>
| style="text-align: center;" | 165
|}
== [[File:Implies.png|Implies]] Implies ==
Accepts two Boolean or [[Numeric|numeric]] inputs.
'''Boolean''': If provided Boolean values, returns [[File:BooleanFalse2010.png|border|False]] if the first input is [[File:BooleanTrue2010.png|border|True]] and the second input is [[File:BooleanFalse2010.png|border|False]]. Otherwise returns [[File:BooleanTrue2010.png|border|True]].
{| class="wikitable"
! x
! y
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanFalse2010.png|border|False]]
| [[File:BooleanFalse2010.png|border|False]]
|-
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
| [[File:BooleanTrue2010.png|border|True]]
|}
'''Numeric''': If provided [[Numeric|numeric]] values performs a bit-wise implies operation.
{| class="wikitable"
!
! Binary
! Decimal
|-
! x
| <code>10101010</code>
| style="text-align: center;" | 170
|-
! y
| <code>11110000</code>
| style="text-align: center;" | 240
|-
! output
| <code>11110101</code>
| style="text-align: center;" | -11
|}
== [[File:Andarray.png|And Array Elements]] And Array Elements ==
Performs the [[#Logical_And|Logical And]] on an n-dimensional [[Array|array]] of Boolean values. This means, the output is [[File:BooleanTrue2010.png|border|True]] if '''all''' elements of the array are [[File:BooleanTrue2010.png|border|True]]. Note that this function works an multi-dimensional arrays, not just one-dimensional.
== [[File:Orarray.png|Or Array Elements]] Or Array Elements ==
Performs the [[#Logical_Or|Logical Or]] on an n-dimensional [[Array|array]] of Boolean values. This means, the output is [[File:BooleanTrue2010.png|border|True]] if '''any''' element of the array is [[File:BooleanTrue2010.png|border|True]]. Note that this function works an multi-dimensional arrays, not just one-dimensional.
== [[File:Numtoboo.png|Num to Array]] Num to Array ==
Converts an [[Integer|integer]] or [[Fixed-point|fixed-point]] number to a Boolean array. The size of the output array depends on the size of the provided number. Note that the least significant bit is at index zero.
== [[File:Bootonum.png|Array to Num]] Array to Num ==
Converts a Boolean array to an [[Integer|integer]] or [[Fixed-point|fixed-point]] number with the least significant bit at index zero.
== [[File:Bootoone.png|Bool to (0,1)]] Bool to (0,1) ==
Returns a Boolean into a 16-bit [[Integer|integer]].
{| class="wikitable"
! x
! output
|-
| [[File:BooleanFalse2010.png|border|False]]
| 0
|-
| [[File:BooleanTrue2010.png|border|True]]
| 1
|}
== [[File:BooleanTrue2010.png|True Constant]] True Constant ==
This is the Boolean True constant [[File:BooleanTrue2010.png|border|True]]
== [[File:BooleanFalse2010.png|False Constant]] False Constant ==
This is the Boolean False constant [[File:BooleanFalse2010.png|border|False]]


== See also ==
== See also ==

Revision as of 17:00, 2 September 2019

AndOrExclusive OrNotCompound ArithmeticNot AndNot OrNot Exclusive OrImpliesAnd Array ElementsOr Array ElementsNum to ArrayArray to NumBool to (0,1)True ConstantFalse Constant
Boolean palette (Click on a function to navigate, or on the arrow to go to parent palette)
Object information
Owning palette(s) Programming palette
Type Palette
Requires Basic Development Environment

The Boolean palette provides constants and functions that can be performed on Boolean, Numeric and Fixed-point values.

Functions

Logical And Logical And
Logical Or Logical Or
Exclusive Or Exclusive Or
Not Not
Compound Arithmetic Compound Arithmetic
Not And Not And
Not Or Not Or
Not Exclusive Or Not Exclusive Or
Implies Implies
And Array Elements And Array Elements
Or Array Elements Or Array Elements
Num to Array Num to Array
Array to Num Array to Num
Bool to (0,1) Bool to (0,1)

Constants

True Constant True Constant
False Constant False Constant

See also

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