Puzzle 81 of 100

A half adder

Goal

Add A and B: make S high while exactly one of them is high, and CO high while both are. The carry is drawn: add the sum.

Die: 32 by 23 squares
Layers: Metal, Polysilicon, Contact, N active, P active, N well, Metal 2, Via
Inputs: A, B
Outputs: CO, S
Supply: VDD
Ground: GND

Go to the solution

New in this puzzle

Adding two bits

One plus one is two, which binary writes as 10: a sum bit of 0 and a carry of 1. A half adder gives both bits. The sum is high when exactly one input is high, and the carry when both are.

Guide

Draw the outlined NOR gate and bring A and B to its gate lines. Its output is high only while both inputs are low.
Draw the second NOR gate in the outlined place, feed it CO and the output of the first one, and join its output to S.

Hint

S is high while A or B is high, except while CO is high. Draw a NOR gate of A and B, then a second NOR gate of CO and the first gate's output; the second gate's output is S.

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 81, A half adder, 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 81, A half adder, 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 81, A half adder, 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

Metal221 squares
Polysilicon65 squares
Contact48 squares
N active26 squares
P active52 squares
N well160 squares
Metal 2156 squares
Via29 squares
Input padA, B
Output padCO, S
Supply padVDD
Ground padGND
Squares you draw, change, or erase182 squares

About the drawing

The drawing uses 438 of the die's 736 squares.
Part of the drawing is in place when the puzzle opens. To finish it, paint 125 empty squares and change 57 drawn squares.
It forms 14 transistors: 7 N transistors and 7 P transistors. Each one is a place where polysilicon crosses active silicon.
48 contacts join metal to the polysilicon or active silicon under it.
29 vias join metal 2 to the metal under it.

Starting drawing for puzzle 81, A half adder, on a numbered grid. — The drawing when the puzzle opens. The dashed outline marks the squares the solution changes.