I'm not sure (not having a full understanding on the electronics behind such a system) whether or not this is a desirable project or experience but it sure is interesting. John Pultorak built a replica of this system and then documented the design to the level of potentially building your own. I'm a bit surprised at the high price but I suppose if he was tinkering around and using better parts that could happen.
http://echoesofapollo.com/resources/apollo-guidance-computer/
http://echoesofapollo.com/resources/apollo-guidance-computer/