ed back into the circuit that computes them. Such feedback loops are used to create "bistable" or two-state logical devices. The corre- sponding devices are called FLIP-FLOP gates, and are activated by a clock signal. A FLIP-FLOP gate can have different output possibilities, or states, depending on (a) the input bits, and (b) the previous state in which it is found at each clock cycle. There exist several types of elementary FLIP-FLOP gates, which find many applications data registers and counters, and computer memories. Finally, any single-port logic gate whose output is equal to the input performs the function REPEAT, as does a "repeater" in digital electronics. This is the case of the CNOT gate with the control bit set to Having, now, an understanding of the various logic gates and functions, it is well worthwhile to provide a basic example of ALU (algorithmic and logical unit) circuitry. Figure 15.6 shows the impressive logical circuit of a four-bit ALU, an integrated circuit from the TTL (transistor-transistor logic) family referred to as 74181. 11 The following does not represent any authoritative description of the '181 (as profes- sionals call it), but simply a brief academic overview. As may be counted from the figure, this ALU network includes 67 logic gates (namely: 38 AND, 12 NOR, 4 XOR, 4 NAND, and 9 NOT). The four-bit inputs A = (A0A1A2A3), B = (BOB1B2B3) (top) and output 10 See, for instance: http://en.wikipedia.org/wiki/Flip-flop_(electronics), http://computer.howstuffworks.com/ boolean3.htm, www.eelab.usyd.edu.au/digital_tutorial/part3/fl-types.htm. See (in French): http://fr.wikipedia.org/wiki/Unit%C3%A9_arithm%C3%A9tique_et_logique. Also see datasheet in (for instance): www.ac-nancy-metz.fr/enseign/ssi/ressourcesP/Documentation/GE/TTL/74hc181.pdf. 15.2 From computer architecture to logic gates Figure 15.6 Basic example of a four-bit ALU (inputs AoA1A2A3, BoB1B2B3, output FFiF2F3). F = (FoFiF2F3) (bottom) are shown in open circles (note that, here, the operands are conventionally input in comple