The Partial 1880 New Jersey Census was made available by the University of Minnesota. I have taken their format, extracted the Partial Newark Census, and reformatted it in an easier to read form. They also have available partial censuses from every state. Please remember that this is a PARTIAL census (approx 1%) and should ONLY be used as a guide. All spellings remain just as they are on the original census form. Please do not email me for further information, I have only what is on these pages. If anyone can decipher their codes I would be more than happy to post the codes here.
Below is part of their instructions on how to use the census:

The only truly "human readable" values are Street Address, and Individual's Surname and forename.  The remainder of the information is held as two- to four-digit codes for use as an index into separate tables giving absolute values.

Briefly, 'H' at the beginning of a record (line) indicates a 'Household' record, which contains information pertaining the household. The remaining fields are a mixture of absolute values, and indexes into separate tables giving overall the following fields, in order:-

County, State, Supervisor's District Number, Enumeration District Number, Month of Enumeration, Day of Enumeration, Microfilm Reel Number, Microfilm Page Number, Dwelling Number, Household Number and Street Address.

Each subsequent record, until the next 'H' record, contains coded information relating to an individual in that household. The original sample data had a 'P' as first character, but we decided this was unnecessary, as all that's necessary is a method of distinguishing 'H' records from any other record.  The first character of an Individual record is always numeric, so that posed no problem - 'H' was unique already!

The Individual record contains absolute values for, or indexes into separate tables for the following fields, in order:-

Race, Sex, Age in Years, Age in Months, General Relationship,
Detailed Relationship, Marital Status, General Occupation (1950
System), Detailed occupation, Sickness on Day of Enumeration,
whether Blind, Deaf and Dumb, Idiotic, Insane, Maimed, Crippled,
Bedridden or Otherwise Disabled, Literacy, Birthplace, Father's
Birthplace, Mother's Birthplace, Individual's Last Name and
Individual's First Name.