Logic Diagrams

What is a Logic Diagram?

A logic diagram is a graphical representation of a digital circuit. It illustrates how logic gates are connected to process binary inputs and produce outputs.

Logic diagrams help engineers design, test, and optimise electronic circuits for computing and automation.

Standard Logic Gate Symbols

Gate Behaviour Symbol
AND Outputs 1 only if both inputs are 1 AND Gate
OR Outputs 1 if at least one input is 1 OR Gate
NOT Inverts the input (0 becomes 1, 1 becomes 0) NOT Gate
NAND Outputs 0 only if both inputs are 1 NAND Gate
NOR Outputs 1 only if both inputs are 0 NOR Gate
XOR Outputs 1 if the inputs are different XOR Gate
XNOR Outputs 1 if the inputs are the same XNOR Gate

Constructing Logic Circuits

Logic diagrams can combine multiple gates to create complex circuits.

  • Combinational Circuits: Output depends only on current inputs.
  • Sequential Circuits: Output depends on both current and previous inputs (uses memory elements).
  • Circuits can be drawn using standard logic symbols and connected with lines to show the data flow from input to output.

Example: Logic Diagram for a Boolean Expression

The Boolean expression F = (A AND B) OR NOT C can be represented as:
Logic Diagram
F represents the Output. Any letter is OK, eg O.
Often, expressions are written simply as: (A AND B) OR NOT C. You decide on the letter to represent the Output.

Truth Table for the Example Logic Diagram

Input A Input B Input C A AND B [D] NOT C [E] F = D OR E
000011
011000
100011
111101

Worked Scenarios: Logic Diagram Construction

Context: A home alarm is triggered (F) if:

  • The door is open (A = 1), and
  • Motion is detected (B = 1), or
  • The system is in override mode (C = 1)

Boolean Expression: F = (A AND B) OR C

Description: The alarm is activated if both the door is open and motion is detected, or if the system is manually overridden.

Logic Diagram 2

Context: A sprinkler system turns on (F) only if:

  • The soil is dry (A = 1),
  • It is not raining (B = 0), and
  • It is daytime (C = 1)

Boolean Expression: F = A AND (NOT B) AND C

Description: All three conditions must be met: dry soil, no rain, and daytime for the sprinkler to activate.

Logic Diagram 3

Simplifying Logic Diagrams

Logic diagrams can be simplified using:

  • Boolean Algebra: Applying logical rules to reduce the number of gates.
  • Karnaugh Maps (K-Maps): A method to minimize Boolean expressions graphically.
  • De Morgan’s Theorems: Useful for simplifying NOT, AND, and OR combinations.

 Key Takeaways

  • Logic diagrams visually represent how logic gates process inputs to produce outputs.
  • Standard gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR.
  • Boolean expressions can be drawn as logic diagrams using standard symbols and wiring.
  • Complex circuits can be simplified using Boolean laws and Karnaugh Maps to optimise design and performance.
  • Logic diagrams form part of the process in developing digital systems such as CPUs, control units, and embedded hardware.