Logic diagram

Also called: logic circuit diagram, gate diagram, logic schematic, gate-level schematic

A drawing of a digital circuit using gate symbols connected by wires, with inputs on the left and outputs on the right.

A logic diagram (or logic schematic) shows a circuit as gate symbols joined by lines that stand for wires. It is the third way to describe a function, next to a boolean expression and a truth table, and it is the one closest to real hardware.

Conventions that almost every diagram follows:

Signals flow left to right. Inputs enter on the left, outputs leave on the right.
Each gate's inputs attach to its back, and its output leaves from its front.
Where a wire splits to feed several gates (fan out), the branch point is often marked with a dot.
Two wires that simply cross without a dot are not connected.
Inversions are drawn as NOT gates or as bubbles on gate pins.

Going from expression to diagram:

Find the outermost operation. It becomes the last gate on the right.
Each operand of that operation is a sub-expression. Draw a gate for each, feeding the last gate.
Repeat until every wire on the left is a plain input or an inverted input.

Going from diagram to expression is circuit analysis. A diagram shows more than the bare function: the number of gates, how many levels deep the circuit is (which affects propagation delay), and which signals are shared.

Worked example

Example

Drawing Y = A'B + C

Turn the expression into a logic diagram, as shown above.

1.
The outermost operation is OR (AND binds tighter), so an OR gate goes on the right.
2.
One OR input is : an AND gate with inputs and B.
3.
needs a NOT gate on A, placed before the AND.
4.
The other OR input is C, wired straight in.
5.
Total: one NOT, one AND, one OR. Check A = 0, B = 1, C = 0: NOT gives 1, AND gives 1, OR gives 1, and = 1. ✓

Common mistakes

Treating crossing wires as joined. Only a dot (or a T-junction) marks a connection.
Starting the drawing from the innermost bracket and losing track of what feeds what. Start from the outermost operation.
Reading a diagram right to left. Signals travel from the inputs on the left to the output on the right.

Practice Logic diagram

Interactive questions with instant feedback and a worked solution for every wrong answer.

Logic Gates lesson

Learn it step by step

Logic diagram is taught in Logic Gates and Combinational Logic.

Logic Gates →Combinational Logic →

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