By Jeffrey D. Ullman
Subject material is split into 3 elements. the 1st covers VLSI-oriented computations. the second one half is orientated to the layout of algorithms. The 3rd a part of the publication issues VLSI layout instruments and the algorithms that underlie them. each one bankruptcy comprises workouts to check the fundamental thoughts and to increase the information of the bankruptcy.
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Extra info for Computational Aspects of VLSI (Principles of Computer Science Series)
The speed of light limits the propagation time no matter what we do. In effect, if we speed up the circuit too much, our model that assumed the time could be measured by the product of the resistance and capacitance loses validity. Fortunately, this effect will not become significant until circuits become somewhat larger, or faster, or both. Light travels roughly a foot in a nanosecond. 006 nanosecond. Since the largest chips in the early 1980's are about 10 millimeters on a side, wires cannot get too much bigger than our example, and the speed of light generally can be ignored.
The voltages under our assumptions, for an inverter fed. by a signal that goes through a pass transistor, such as a clocking gate, are shown in Fig. 16(a). 3 ELECTRICAL PROPERTIES OF CIRCUITS 5 1 5 [; ~ 5 5/9 j5 0 (a) 0 (b) Fig. 16. Voltages on an inverter. 5 voltst is ample to keep the pulidown on, and at close to the lowest resistance it could ever be. Fig. 16(b) shows an inverter whose input is at 5 volts rather than 4 and whose pullup/pulldown resistance ratio is 4:1 rather than 8:1. 5 in Fig.
This rule is particularly relevant when the element is a contact. As grid points have only four adjacent grid edges, we cannot bring an arbitrary number of wires to an element; we are limited to four times the number of layers permitted, and even that number may not be a realistic limit, say for a contact. If we need more wires impinging on a circuit element than can connect to a single grid point, we may represent the circuit element by a rectangle covering as many grid points as needed. We assume for convenience that wires carry signals in one direction only, so it makes sense to speak of inputs and outputs of logic elements.
Computational Aspects of VLSI (Principles of Computer Science Series) by Jeffrey D. Ullman