Under the heading state, we know that there are 48 states, the District of Columbia, and several territories and possessions—all told, perhaps 60 possibilities. So, 2 punch-card columns are enough: they will allow 100 different sets of punches from 00 to 99 to be put in them. We then assign the _code_ 00 to Maine, 01 to New Hampshire, 02 to Vermont, etc., or we might assign the code 00 to Alabama, 01 to Arizona, 02 to Arkansas, etc.—whichever would be more useful. Under the other headings, we do the same thing: count the possibilities; assign codes. In this case, it will be reasonable to use numeric codes 0 to 9 in each column in all places because we shall have millions of cards to deal with and numeric codes can be sorted faster than alphabetic codes. Alphabetic codes require 2 punched holes in each column, and sorting any column takes 2 operations. The punch cards are printed with the chosen headings. We set up the codes in charts and give them to clerks. Using key punches and verifiers, they punch up the cards and check them. They work from the original information collected by the census-taker in the field. Since the original information will come in geographically, probably only one geographic code at a time will be needed, and it will be simple to keep track of. As to occupation, however, it may be useful to assign other clerks full-time to examining the original information and specifying the right code for the occupation. Then the clerks who do the punching will have only copying to do. The great bulk of the work with the census will be sorting, counting, and totaling. The original punch cards will be summarized into larger and larger groups. For example, the cards for all males age 23 last birthday living in the state of Massachusetts are sorted together. This group of cards may be put into a tabulator wired to a summary punch. When the tabulator has counted the last card of this group, the summary punch punches one card, showing the total number in this group. Some time later a card like this will be ready for every state. Then the whole group of state cards may be fed into the tabulator wired to the reproducer acting as summary punch. When totaled, the number of males age 23 last birthday in the United States will be punched into a single card. After more compiling, a card like this will be ready for all males in the United States at each age. Then this group of cards may be fed into the tabulator wired to the summary punch. Each card may be listed by the tabulator on the paper flowing through it, showing the age and the number of males living at that age. At the end of the listing, the tabulator will print the total number of all males in the list, and the summary punch will punch a card containing this total. ARITHMETICAL OPERATIONS Punch-card machines can perform the arithmetical operations of counting, adding, subtracting, multiplying, dividing, and rounding off. Counting