The systematic reduction of logic circuits is accomplished using Boolean algebra.

Boolean algebra is a mathematical system that deals with logic operations and variables that can have only two values - true or false. It provides a set of rules and operations that can be used to simplify and manipulate logic circuits.

There are several techniques used in the systematic reduction of logic circuits using Boolean algebra:

1. Boolean Identities:
- Theorems and properties of Boolean algebra, such as the commutative, associative, and distributive laws, can be applied to simplify logic expressions.
- These identities allow for the rearrangement and combination of logic gates to reduce the complexity of the circuit.

2. Boolean Simplification Techniques:
- Boolean algebra provides techniques like Boolean theorems, Karnaugh maps, and Quine-McCluskey method that can be used to simplify logic expressions.
- These techniques involve finding common terms, combining redundant terms, and eliminating unnecessary gates or variables.

3. De Morgan's Theorems:
- De Morgan's theorems are a set of rules that allow for the conversion between logic gates.
- They state that the complement of a logic expression involving AND, OR, or NOT gates can be obtained by interchanging the gates and complementing the inputs or outputs.

4. Truth Tables:
- Truth tables are used to represent the behavior of logic circuits.
- By systematically evaluating the truth table and identifying patterns, redundancies, or simplifications, logic expressions can be simplified.

The systematic reduction of logic circuits using Boolean algebra allows for the simplification and optimization of complex circuits. This reduction process helps in reducing the number of gates, reducing power consumption, reducing propagation delays, and improving the overall performance of the circuit. It is an essential technique in digital design and is widely used in the field of electrical engineering.