Objectives: Digital Logic

● ref: [Tanembaum, ch 3]

● to know the gates corresponding to digital logic operations, and how these can be

constructed from transistors

● to understand how more complex circuits (e.g. an adder in an ALU) can be

constructed by a circuit of such gates

● to be able to derive the truth table for such a circuit (and the converse, in simple

cases)

● to understand how bits can be implemented using feedback circuits, and how

registers may be constructed

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Gates

● digital logic is lowest level of computer organization!

● digital circuit elements (including 1-bit memory cells) are made from gates

(in turn, from 1 or more transistors or switches, see this appendix)

● [Null&Lobor, figs 3.1-2]: AND and OR gates manipulate voltage levels (0- low, 1 -

high) according to truth tables (Boolean logic)

● [O’H&Bryant, p 45]: set of colors forming an 8-element boolean algebra

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Half Adders

● from gates, higher-level components such as a half-adder are constructed

([Null&Lobor, figs 3.10,3.11]: Sum = X XOR Y, Carry = X AND Y)

● this can be extended to a full adder ([Null&Lobor, fig 3.13])

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