DIGI-COMP I ("one") is a mechanical calculation device, delivered in kit form. Originally manufactured from polystyrene parts by E.S.R. Inc starting in 1963, it is as old as I am!
It was sold as an educational toy for just $4.99. Sales passed 100.000 and stopped in the 1970s with the rise of electronic toys.
There are many reference on the web, start with https://en.wikipedia.org/wiki/Digi-Comp_I and E.S.R.

DIGICOMP I is quite small: Dimensions are 31 cm x 8 cm x 12 cm. It consists of a mechanical 3 bit memory and programmable logic.
As an "electronic guy", I always was fascinated by mechnical calculation ... powered by a general lack of understanding. DIGICOMP came into my life after a speach about the arithmetic logic in Zuse Z1 (Klemens Krause on VCFB 2019).
Here it is running here (driven by a self-built motor), programmed to implement a binary counter:
This "binary counter" application as well as detailed functions are found in the user's manual, see attachement.
And: DIGI-COMP I is not to be confused with DIGI-COMP II ... that one is a nice looking marble calculator, but not programmable.
The Original Package
In Xmas 1963, you'd find DIGI-COMP I under your tree in this package (picture stolen from a recent eBay offer):

The user manual itself is a retro-futuristic gem and contributes greatly to DIGI-COMPs success.

Today the manual acts also a time machine far back. Given the age of 1963, the rockets images are not yet inspired by the Saturn V moon-reacher .. .we're still in the Mercury aera here.
Six years later we had a man on the moon, and these well-behaved middle-class kids are lying stoned in the mud at Woodstock.
The 60's were quite dynamic!
The Kit
DIGICOMP came as a DIY kit, as a bunch of plastic parts and a few wire rods.

You had to assemble all these before use, anticipating our IKEA experiences. And you can 3D print most parts easily today.
Community
In its prime time DIGICOMP had a big community, selected user games and problems were published by E.S.R. in add-on manuals.
Apparently there's still a fan group for DIGI-COMP and similar devices at Yahoo: "FriendsOfDigicomp". I wasn't able to find their message digest, but their file archive is here:
https://archive.org/details/digicomp_i/mode/2up
Some interesting documents are attached below.
Modern Implementions
DIGI-COMP is still fascinating people, there are several projects around it. I found these links to be active in 2020:
3D prints
DIGI-COMP I can easily reproduced on 3D printers, because all parts are plastic and flat. For example see this project:

Very important: Thanks to these guys, it's easy to replace a broken 1963 part with own prints. Long life DIGI-COMP!
DIGI-COMP I REDUX
This is another project for 3D printer, but a modified design:
https://www.instructables.com/id/Digi-Comp-I-Redux
Minds-On Toys Digi-Comp v2.0
This one is commercial. DIGI-COMP is made from card board instead of plastic.
http://mindsontoys.com/kits.htm?dc1_main.htm
Check out their site, lots of good info.
Online simulator
This is a web based simulator.
https://digicomp-1.appspot.com
You can develop own logic programs, and save and reload them later.
LEGO
Of course! http://www.nico71.fr/lego-computer-digicomp/
digi-comp-1-instruction.pdf -- DIGI-COMP I User Manual
digi-comp-1-parts.pdf -- DIGI-COMP I Part List
coding-sheet.pdf -- DIGI-COMP I Coding Sheet as PDF Form
DC1 Detailed Programming.PDF -- DIGI-COMP I Detailed Programming
DC1-PLA.pdf -- DIGI-COMP I as PLA (by friendsofdigicomp)
Duerig.PDF -- DIGI-COMP I Personal Narrative about Invention and Marketing (friendsofdigicomp)
Patent_03273794.pdf -- DIGI-COMP I Patent Original (friendsofdigicomp)