5.3 Combinational Gates

• A combinational gate is an abstract representation of a circuit that satisfies two properties:

1. Its outputs are a function of its inputs alone.

2. It satisfies the static discipline.

5.2 Boolean Logic

5.1 Voltage Levels and Static Discipline

• To send a logical 0, the sender must produce an output voltage value that is less than VOL. Correspondingly, the receiver must interpret input voltages below VIL as a logical 0.
• Similarly, to send a logical 1, the sender must produce an output voltage value that is greater than VOH. Further, the receiver must interpret voltages above VIH as a logical 1.
• Noise Margin: The absolute value of the difference between the prescribed output voltage for a given logical value and the corresponding forbidden region voltage threshold for the receiver is called the noise margin for that logical value.
• NM0 = VIL − VOL
• NM1 = VOH − VIH
• The static discipline is a specification for digital devices. The static discipline requires devices to interpret correctly voltages that fall within the input thresholds (VIL and VIH). As long as valid inputs are provided to the devices, the discipline also requires the devices to produce valid output voltages that satisfy the output thresholds (VOL and VOH).

5.0 The Digital Abstraction

• Value discretization forms the basis of the digital abstraction
• Although the digital approach seems wasteful of signal dynamic range, it has a significant advantage over analog transmission in the presence of noise

4.5 Incremental Analysis

• Process of linearizing device models over a very narrow operating range is called incremental analysis
• Systematic procedure for finding incremental voltages and currents for a circuit with a nonlinear device characterized by the v-i relation iD = f(vD) :

4.4 Piecewise Linear Analysis

• Piecewise linear analysis represents the nonlinear v-i characteristics of each nonlinear element by a succession of straight-line segments, then make calculations within eachstraight-line segment using the linear analysis tools already developed

4.3 Graphical Analysis

• There are many nonlinear circuits that cannot be solved analytically. Usually we must resort to trial-and-error solutions on a computer. Such solutions provide answers, but usually give little insight about circuit performance and design. Graphical solutions, on the other hand, provide insight at the expense of accuracy

• For circuits with two nonlinear elements, the method is less useful, as it involves sketching one nonlinear characteristic on another. Nonetheless, crude sketches can still provide much insight
• Assuming E = 3 V, R = 500 ohm