1/16/ CSEE, UQ Lecture 3 Hardware Description Methods, Review of Switching Algebra

1/16/ CSEE, UQ x1=x0= (a) Two states of a switch S x (b) Symbol for a switch A binary switch

1/16/ CSEE, UQ (a) Simple connection to a battery S x (b) Using a ground connection as the return path L BatteryLight x Power supply S L A light controlled by a switch

1/16/ CSEE, UQ (a) The logical AND function (series connection) S x 1 L Power supply S x 2 S x 1 L Power supplyS x 2 (b) The logical OR function (parallel connection) Light Two basic functions

1/16/ CSEE, UQ S x 1 L Power supplyS x 2 Light S x 3 A series parallel connection

1/16/ CSEE, UQ S x L Power supply R An inverting circuit

1/16/ CSEE, UQ Truth table for AND and OR

1/16/ CSEE, UQ Three input AND and OR

1/16/ CSEE, UQ x 1 x 2 x n x 1 x 2 x 1 x 2. x 1 x 2 … x n. (a) AND gates (b) OR gates x 1 x 2 x 1 x 2 + x 1 x 2 x n x 1 x 2 … x n +++ Basic gates x x (c) NOT gate x 1 x 2 x 1 x 2. x 1 x 2 x 1 x 2 + (d) NAND gate (e) NOR gate

1/16/ CSEE, UQ x 1 x f (a) Network that implements fx1x1 x1x1 x2x2 += x 1 x 2 fx 1 x 2,() (b) Truth table for f A B Logic network

1/16/ CSEE, UQ x 1 x 2 A B f Time (c) Timing diagram g x 1 x 2 (d) Network that implementsgx 1 x 2 += Logic network

1/16/ CSEE, UQ Boolean algebra - axioms 0*0 = = 1 1*1 = = 0 0* 1 = 1* 0 = = = 1 x*0 = 0 x + 1 = 1 x*1 = x x +0 = x x* x = x x + x = x x* x = 0 x+ x = 1 x = x x*y = x + y x + y = x*y x + x*y = x + y x*(x + y) = x*y DeMorgan laws

1/16/ CSEE, UQ DeMorgan’s theorem

1/16/ CSEE, UQ Figure 2.12 The Venn diagram representation Please see “portrait orientation” PowerPoint file for Chapter 2

1/16/ CSEE, UQ Figure 2.13 Verification of the distributive property Please see “portrait orientation” PowerPoint file for Chapter 2

1/16/ CSEE, UQ Please see “portrait orientation” PowerPoint file for Chapter 2 Figure 2.14 Verification example

1/16/ CSEE, UQ A function to be synthesised

1/16/ CSEE, UQ f (a) Canonical sum-of-products f (b) Minimal-cost realization x 2 x 1 x 1 x 2 Two implementations

1/16/ CSEE, UQ Minterms and maxterms

1/16/ CSEE, UQ A three variable function

1/16/ CSEE, UQ (a) A minimal sum-of-products (b) A minimal product-of-sums f x 1 x 2 x 3 f x 2 x 1 x 3 Two implementations

1/16/ CSEE, UQ Three way light controller A room with three doors. Light switch at each door. Light turned on/off at each door. 1 - turned on. 0 – turned off. Specification (for logic only):

1/16/ CSEE, UQ f x 1 x 2 x 3 Sum of Products – SOP

1/16/ CSEE, UQ f x 1 x 2 x 3 Products of Sums – POS

1/16/ CSEE, UQ (a) Truth table f s x 1 x (c) Graphical symbol (b) Circuit (d) More compact truth table sx1x1 x2x2 f (s, x 1, x 2 ) 0 1 s x1x1 x2x2 f x 1 x 2 s Multiplexer

1/16/ CSEE, UQ (a) Truth table (c) XOR Graphical symbol (b) One of XOR Circuits XOR, XNOR gates x1x1 x2x2 XOR XNOR f x 1 x 2 (d) XNOR Graphical symbol

1/16/ CSEE, UQ Waveform Editor

1/16/ CSEE, UQ Graphic Editor

1/16/ CSEE, UQ Please see “portrait orientation” PowerPoint file for Chapter 2

1/16/ CSEE, UQ f x 3 x 1 x 2 first touch of VHDL

1/16/ CSEE, UQ A bit more of VHDL

1/16/ CSEE, UQ f g x 3 x 1 x 2 x 4 Four-input function