PYTHON · NUMPY

Synthesize: Fewer Gates

Take a function written as a raw sum of every true row and factor it into far fewer gates — what logic synthesis (Yosys) does for a living.

01Challenge

A function is given as its truth table (a sum of minterms). That form is correct but wasteful. Factor it into an equivalent expression with fewer gates — same truth table, less silicon.

Predict firstA synthesizer turns your Verilog into a gate netlist. Writing the SAME logic a different way in Verilog usually gives…

02Model

When you write RTL, you don't place gates — a synthesis tool does, and its whole job is to find the cheapest gate network that matches your truth table. The naive form is a 'sum of products': one AND per true row, all OR'd together. Synthesis factors shared terms out. f = (a AND b) OR (a AND c) has two AND gates and an OR; factor the common a and it becomes a AND (b OR c) — one AND, one OR. Same function, fewer gates, less area, less power. That is synthesis in one move.

03Guided practice

Worked: define f_ref from minterms and count them. Faded: write f_min as a factored expression. Independent: prove f_min equals f_ref on all 8 rows and uses fewer gates.

04Feedback

PASS WHEN You matched the truth table with far fewer gates — the essence of what a synthesizer does to your RTL.

If your run fails, check:

FAIL: not equivalent — check f_min against every row of the truth table.
FAIL: no gate savings — pull the common factor (a) out of the two product terms.

05Retrieve & space

What does a synthesis tool optimize? (The gate network — fewer/smaller gates for the same truth table.)
What did factoring 'a' out save? (One gate, and with it area and power.)
What real tool does this in the open flow? (Yosys.)

06Mastery & project

Reduces a sum-of-minterms function to an equivalent, smaller gate network (L2: logic minimization, the core of synthesis).

Fewer gates means less area and power — the first half of the PPA story the next lesson finishes with timing.

← Write It in Verilog The Critical Path →

PYTHON · NUMPY

Synthesize: Fewer Gates

Factor a sum-of-minterms function into fewer gates, proving equivalence.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you