Puzzle 89 of 100

A parity tree

Goal

Make Y high while an odd number of A, B, C, and D are high, at least as fast as the target. Three exclusive OR gates are drawn: wire them.

Die: 48 by 21 squares
Layers: Metal, Polysilicon, Contact, N active, P active, N well, Metal 2, Via
Inputs: A, B, C, D
Output: Y
Supply: VDD
Ground: GND

Go to the solution

New in this puzzle

A balanced tree

An exclusive OR of four inputs needs three gates. In a chain the slowest input passes through all three; in a tree every input passes through two, so the result arrives sooner.

Hint

In a chain of three gates, the first inputs pass through all three. Pair the inputs instead: one gate for A and B, one for C and D, and the gate in the middle for their two outputs.

Solution

This is the game's reference drawing for the puzzle. It meets the goal and passes the design rules. Other drawings can pass as well.

Top View of the solved die for puzzle 89, A parity tree, with the Side View below it. — Top View of the solved die, captured from the game. Paths that carry a high level at the moment shown are lit. The Side View below cuts through the row between the dashed lines.

The game window in Isometric View with the solved die for puzzle 89, A parity tree, the guide, and the scope. — The whole game window in Isometric View. The scope on the right compares each output with its target band, and the message above it confirms that the drawing passes.

Solution drawing for puzzle 89, A parity tree, drawn on a numbered grid with every layer in its game color and pattern. — The solution on the grid. Squares are numbered from the top left corner, so you can count them. The dashed outline marks the squares you draw, change, or erase; the rest is drawn when the puzzle opens.

Legend

Metal319 squares
Polysilicon120 squares
Contact69 squares
N active42 squares
P active78 squares
N well144 squares
Metal 2300 squares
Via59 squares
Input padA, B, C, D
Output padY
Supply padVDD
Ground padGND
Squares you draw, change, or erase290 squares

About the drawing

The drawing uses 634 of the die's 1008 squares.
Part of the drawing is in place when the puzzle opens. To finish it, paint 218 empty squares and change 72 drawn squares.
It forms 30 transistors: 15 N transistors and 15 P transistors. Each one is a place where polysilicon crosses active silicon.
69 contacts join metal to the polysilicon or active silicon under it.
59 vias join metal 2 to the metal under it.

Starting drawing for puzzle 89, A parity tree, on a numbered grid. — The drawing when the puzzle opens. The dashed outline marks the squares the solution changes.