---
categories:
  - Logic
  - Computer Architecture
tags: [logic, propositional-logic, nand-to-tetris]
---

# Boolean function synthesis

When we looked at [boolean functions](/Logic/Propositional_logic/Boolean_functions.md) we were working in a particular direction: from a function to a truth table. When we do Boolean function synthesis we work in the opposite direction: from a function to a truth table.

This is an important skill that we will use when constructing [logic circuits](/Electronics_and_Hardware/Digital_circuits/Digital_circuits.md). We will go from truth conditions (i.e. what we want the circuit to do and when we want it to do it) to a function expression which is then reduced and implemented with [logic gates](/Electronics_and_Hardware/Digital_circuits/Logic_gates.md).

## The process

The process proceeds as follows: