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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
COMP2300: Digital Logic 2015 ◭◭ ◭ • ◮ ◮◮ × 1
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
COMP2300: Digital Logic 2015 ◭◭ ◭ • ◮ ◮◮ × 2
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])
COMP2300: Digital Logic 2015 ◭◭ ◭ • ◮ ◮◮ × 3