30CHAPTER 3. LOGIC GATES3.1Digital signals and gatesWhile the binary numeration system is an interesting mathematical abstraction, we haven’t yet seenits practical application to electronics. This chapter is devoted to just that: practically applying theconcept of binary bits to circuits. What makes binary numeration so important to the application ofdigital electronics is the ease in which bits may be represented in physical terms. Because a binarybit can only have one of two diﬀerent values, either 0 or 1, any physical medium capable of switchingbetween two saturated states may be used to represent a bit. Consequently, any physical systemcapable of representing binary bits is able to represent numerical quantities, and potentially has theability to manipulate those numbers. This is the basic concept underlying digital computing.Electronic circuits are physical systems that lend themselves well to the representation of binarynumbers. Transistors, when operated at their bias limits, may be in one of two diﬀerent states:either cutoﬀ (no controlled current) or saturation (maximum controlled current). If a transistorcircuit is designed to maximize the probability of falling into either one of these states (and notoperating in the linear, or active, mode), it can serve as a physical representation of a binary bit. Avoltage signal measured at the output of such a circuit may also serve as a representation of a singlebit, a low voltage representing a binary ”0” and a (relatively) high voltage representing a binary”1.” Note the following transistor circuit:5 VVin = 5 VVout ≈ 0 V0 V = "low" logic level (0)"high" input5 V = "high" logic level (1)"low" outputTransistor in saturationIn this circuit, the transistor is in a state of saturation by virtue of the applied input voltage(5 volts) through the two-position switch. Because it’s saturated, the transistor drops very littlevoltage between collector and emitter, resulting in an output voltage of (practically) 0 volts. Ifwe were using this circuit to represent binary bits, we would say that the input signal is a binary”1” and that the output signal is a binary ”0.” Any voltage close to full supply voltage (measuredin reference to ground, of course) is considered a ”1” and a lack of voltage is considered a ”0.”Alternative terms for these voltage levels are high (same as a binary ”1”) and low (same as a binary”0”). A general term for the representation of a binary bit by a circuit voltage is logic level.Moving the switch to the other position, we apply a binary ”0” to the input and receive a binary”1” at the output: