You are quite right, unfortunately. It just can't be done. To add with an adder matrix, you need "storages" - storages in which the pulses of coded numbers can be kept until they are needed.
We cannot tell you here what such a storage looks like. This will be described in the next chapter. Meanwhile you will just have to take our word for it that there are such things; imagine them as little railway sidings in which electric pulses can be kept waiting for a short time, and from which they can be brought out when the order is given. That, in fact, is the principle on which they are designed.
The first thing our computer does with the grocery bill is to extract the 36 items from the punched tape and put them into its storage. Counting does not start until then. The storage locations of the first two numbers are connected to the adder matrix, added up there and forwarded as a total to an empty place in the storage. This is the first stage.
Second stage: the first total just stored is sent again into the adder matrix. In the same fraction of a second, the third item in the bill runs from its storage place on the other side into the matrix. The first total and the third number are added up to a new total, which is also stored.
Third stage: the new total and the fourth stored number are added together . . . and the computer proceeds in the same way until all 36 numbers are added up. The last total, the final one, is stored once more. From the storage it is then sent to a teleprinter or a tape punch or into a magnetic tape, to just the place where it is wanted so that it can be typed for the customer on a bill, or - likewise electronically - deducted from his account.
Incidentally, even if the matrix did not make it necessary, you would, first of all, keep the numbers from the punched tape in storages. As we shall see later, there are computers which can count without matrices and which therefore need no storages for them. But in fact they do have them, so that they can accommodate all the data in a bill.
The reason for this storage is once again the fact that the computer speeds vary so much. The arithmetic units of different electronic brains work it is true, at varying speeds, but always much more quickly than a sensing element for punched tape.