Let us check this circuit. First, if there is any operation other than 01 stored in the _C_4 relays, then no current will be able to get through the _C_4 contacts shown and into the _C_5 relay coils, and the result is blank. Second, if we have the operation 01 stored in the _C_4 relays, then the _C_4-2 contacts will not be energized—a condition which passes current—and the _C_4-1 contacts will be energized—another condition which passes current—and: IF THE NUMBER AND THE _C_5 RELAYS IN _C_1 IS: THEN _C_1-1: AND _C_1-2: ENERGIZED ARE: 0 does not close does not close neither 1 closes does not close _C_5-2, _C_5-1 2 does not close closes _C_5-2 only 3 closes closes _C_5-1 only Thus we have shown that this circuit is correct. We see that this circuit uses more than one set of contacts for several relays (_C_1-2, _C_4-1, _C_4-2); relays are regularly made with 4, 6, or 12 sets of contacts arranged side by side, all controlled by the same pickup coil. These are called 4-, 6-, or 12-_pole_ relays. [Illustration: FIG. 9. Addition circuit.] [Illustration: FIG. 10. Greater-than circuit.] Circuits for _addition_, _greater than_, and _selection_ can also be determined rather easily (see Figs. 9, 10, 11). (_Note_: By means of the _algebra of logic_, referred to in Chapter 9 and Supplement 2, the conditions for many relay circuits, as well as the circuit itself, may be expressed algebraically, and the two expressions may be checked by a mathematical process.) For example, let us check that the addition circuit in Fig. 9 will enable us to add 1 and 2 and obtain 3. We take a colored pencil and draw closed the contacts for _C_1-1 (since _C_1 holds 01) and for _C_2-2 (since _C_2 holds 10). Then, when we trace through the circuit, remembering that addition is stored as 00 in the _C_4 relays, we find that both the _C_5 relays are energized. Hence _C_5 holds 11, which is 3. Thus Simon can add 1 and 2 and make 3! [Illustration: FIG. 11. Selection Circuit.] PUTTING SIMON TOGETHER In order to put Simon together and make him work, not very much is needed. On the outside of Simon we shall need two small mechanisms for reading punched paper tape. Inside Simon, there will be about 50 relays and perhaps 100 feet of wire for connecting them. In addition to the 15 registers (_I_, _S_1 to _S_8, _C_1 to _C_5, and _O_), we shall need a register of 4 relays, which we shall call the _program register_. This register will store the successive instructions read off the program tape. We can call the 4 relays of this register _P_8, _P_4, _P_2, _P_1. For example, if the _P_8 and _P_2 relays are energized, the register holds 1010, and this is the program instruction that calls for the 8th plus 2nd, or 10th, register, which is _C_1.