Relay logic
Relay logic
Relay logic is a way of to use combinational logic in electrical control circuits via many electrical relays wired in a configuration.
All techs used in communications, computing and entertainment rest on digital logic.
Embedded Files
Boolean algebra
Boolean algebra
Symbols/Notations
Symbols/Notations
Boolean algebra:
OR = '+', e.g. A + B = "A OR B"
AND = '·' (or implied concatenation, e.g., AB), e.g. A · B or AB = "A AND B"
NOT: '¬', '~', or ' (prime), e.g. : ¬A or A' = "NOT A"
Formal logics (philosophy/symbolic logic) use
OR: ∨ (vee), e.g., A ∨ B
AND: ∧ (wedge), e.g., A ∧ B
NOT: ¬ or ~, e.g., ¬A or [1.6] Ā
Programming languages
OR = || (double pipe), e.g., A || B (C, Java, Python, etc.)
AND = && (double ampersand), e.g., A && B
NOT = !, e.g., !A
Electronics/Electromagnetics/digital Circuits
OR: + (Boolean style) or | (pipe), e.g., A + B or A | B in datasheets.
AND: · or &, e.g., A & B (common in IC datasheets).
NOT: ! or ~, e.g., !A (active-low signals).
Ladder logic (PLC/Relay Diagrams)
OR: parallel branches
plaintext
----[ ]---- (NO Contact A)
| |
----[ ]---- (NO Contact B) → Output
AND: Series contacts
plaintext
----[ ]----[ ]---- (A AND B) → Output
NOT: NC (Normally Closed) contacts
plaintext
----[/]---- (NC Contact A) → Output
Electromagnetic control
Electromagnetic control
[2]
Relay logic in electromagnetic control refers to a method of implementing control systems using electromechanical relays to create logical operations (AND, OR, NOT, etc.) for automating machinery or industrial processes, often done prior programmable logic controllers (PLCs) became dominant.
Logic states
Logic states
When the switch symbol is "lifted," it's "OFF".
When the switch symbol is "closed," it's "ON".
ON (1, TRUE, energized) means a coil is powered, causing contacts to change state.--current flows by default.
OFF (0, FALSE, de-energized) means a coil is unpowered, contacts remain in default state--no Normally Closed (NC) Contact:
Logic relay also use the normally closed and open terms for electric switches--depending on a switch's behavior (NO or NC),
Normally open (NO) contact:
OFF (0) = open circuit (no current flows)
ON (1) = closed circuit (current flows when coil energizes)
Normally closed (NC) contact:
OFF (0) = closed circuit (current flows by default)
ON (1) = open circuit (current stops when coil energizes)
Logic implementation
Logic implementation
Logic implementation is method/techg used to physically realize Boolean logic (e.g., relays, transistors, fluidics, or software).
implementation = the process to decide/plan into effect; execution
"AND" logic is 2 relays in series (both must energize to complete the circuit).
"OR" logic: Two relays in parallel (either can energize to complete the circuit).
"NOT" logic is A normally closed (NC) contact inverts the signal.
E.g. What does it take to turn on the pilot light?
Neither won't work.
This works.
The switches control individual relay coils.
The lamp is controlled by contacts from the relays.
In this case, everything is fed from the same source.
Note the relay contact operation.
This is a control circuit for a return air fan, controlled by a building automation system (BAS).
The return fan must never run if the supply fan isn't.
Logic gate
Logic gate
A logic gate is a basic building block of digital circuits doing a Boolean operation (AND, OR, NOT, etc.) on binary inputs (1s and 0s).
A logic gate is a type of basi digital circuit using binary inputs and makes a binary output, used in digital systems to do operations on binary variables.
Logic functions are often called Boolean functions.
Truth table
Truth table
A truth table is a mathematical table showing all possible input a logic circuit and corresponding outputs' combinations. Relay logic's inputs are often switch/relay contact states (ON/OFF or 1/0).
We can label devices by letters.
A truth table has a device's possible states.
Sizes A truth table's number of rows depends on its number of variables:
1 variable had 2 rows
2 variables had 4 rows
3 variables had 8 rows
4 variable needs 16.
Recall: 'n' = number of variables.
Pattern Use a standard table layout 'and.'
Treat each row as a binary number
The numbers go from 0.
E.g. Row 6 has 1 times 4 plus 1 times: 4 +1, 1 = 5
This function can be written as either:
not A
[1.6] Ā
'AND' usages
We use truth tables to show a circuit's possibilities.
A is off
B is off
This function's output is off.
Another possibility"
A is off but B is on: the light is still off.
Turn A on and B off
The light is still off.
Turn A on and B on
Now the light comes on.
This function can be written as either:
"A and B"
"AB"
"A ∧ B (logical conjunction)"
'OR' usages
For '0,' this function can be written as:
"A or B or C"
"A ∨ B ∨ C" (logical (inclusive) disjunction)
"A + B + C"
Recall: + = "or"
Examples
Examples
E.g. 1# How do we represent this set of switches via symbolic logic?
A and B are in series--looks like an AND
A AND B parallel C--looks like an OR
(A⌐B) + C; or
Note: "a bar over letter B" symbol doesn't exist
E.g. 2# How do we represent this set of switches via symbolic logic?
((⌐A ⌐B) + C)D
What can the truth table for this look like?
If we don’t operate D, the function is 'false'.
If we operate only D, the function is 'true'.
D and C--the function is 'true'.
This gives '0'.
D and C - the function is 'true'.
This is true no matter what happens to A and B.
These 3 all have D true, C false and some A and B.
What is the function?
Simplification E.g. 3# How can we represent this truth table via symbolic logic?
A ⌐B⌐C + A⌐BC + AB⌐C)
A (⌐B⌐C + ⌐BC + B⌐C)
This can be simplified as: A (⌐B + B⌐C)
Karnaugh mapping
Karnaugh mapping
[1.7] A Karnaugh map is
They simplify more complex expressions, are effectively limited to 6 variables, and can’t be readily automated.
This is a generic function.
If 'A' and 'B' both = 0, the function has a value of 'a'.
Map this to the map where:
A and B = 0
Where does b map to?
Where does c map to?
Where does d map to?
Advanced
This method can be done via 3-4 variables. This is a basic map of 3 variables.
8 lines on the truth table and 8 squares in the Karnaugh map.
Note: The truth table's numbers don't increase numerically
Map A = B = C = 0
Map A = B = 0, C = 1
Going across AB, we can only change a value at a time.
The completed table (this is one of the many ways)
An alternative: Columns are now labelled via BC
Rows are now A and not A.
The truth table is labelled CBA
Start by C = B = A = 0,
then by C = B = 0 and A = 1,
C = A = 0, and B = 1.
Via ladder diagrams
[3] Control relays A, B and C via toggle switches:
Lamp 1 is on if:
Switches A and B are closed but not C; or
Switch B closes but not A and C; or
Switch A closes but not B and C.
To truth tables
Switches A and B close but not C or
Switch B closes but not A and C or
Switch A closes but not B and C.
Reading
This pair tells us this function is true if (B and not C) is true--regardless of A.
⌐AB⌐C + AB⌐C reduces to B⌐C
We get this pair by wrapping the map into a cylinder, telling us this function is true if (A and not C) is true--regardless of B.
AB⌐C + ⌐AB⌐C reduces to A⌐C
Ladder diagram simplification
The function reduces to (B and not C) or (A and not C).
The diagram can still be simplified
Real world analogies
Real world analogies
[3] Slide 99
History
History
[2]
Ladder logic
Ladder logic
Related pages
Related pages
References
References
[1] Wikipedia
[1.1] Logic
[1.2] Relay
[1.3] Boolean function
[1.4] Karnaugh map
[1.5] Logic gate
[1.6] Ā
[1.7] Karnaugh map
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