Higher Engineering Mathematics
102 NUMBER AND ALGEBRA 11.5 Karnaugh maps (i) Two-variable Karnaugh maps A truth table for a two-variable expression is shown in ...
BOOLEAN ALGEBRA AND LOGIC CIRCUITS 103 A a couple is given by those variables common to all cells in the couple. See Problems 15 ...
104 NUMBER AND ALGEBRA Table 11.13 110 010 01 P Q (b) The termP·Qis marked witha1inthetopleft- hand cell, corresponding toP=0 an ...
BOOLEAN ALGEBRA AND LOGIC CIRCUITS 105 A Thus: (P+Q·R)+(P·Q+R)=P+Q·R Table 11.16 (a) (b) 4 1 4 2 3 1 4 (^11) 3 2 3 2 3 1 3 (^01) ...
106 NUMBER AND ALGEBRA A·B·C·D+A·B·C·D+A·B·C·D+ A·B·C·D+A·B·C·D [A·D+A·B·C·D] A·B·C·D+A·B·C·D+A·B·C·D+ A·B·C·D+A·B·C·D+A·B·C·D+ ...
BOOLEAN ALGEBRA AND LOGIC CIRCUITS 107 A ‘1’ output and vice versa, i.e. it is an ‘opposite to’ function. The invert ofAis writt ...
108 NUMBER AND ALGEBRA With reference to Fig. 11.24 aninvert-gate, shown as (1), givesB. Theand-gate, shown as (2), has inputs o ...
BOOLEAN ALGEBRA AND LOGIC CIRCUITS 109 A Figure 11.27 Now try the following exercise. Exercise 50 Further problems on logic circ ...
110 NUMBER AND ALGEBRA Column 6 of Table 11.20 [Z 3 =A·C+B, see Fig. 11.29(c)] In Problems 8 to 12, simplify the Boolean expres ...
BOOLEAN ALGEBRA AND LOGIC CIRCUITS 111 A Figure 11.32 produced. Inputs ofA,B, andCto anor-gate give an output ofA+B+C. By de Mor ...
112 NUMBER AND ALGEBRA Problem 27. Usenor-gates only to design a logic circuit to meet the requirements of the expression:Z=D·(A ...
BOOLEAN ALGEBRA AND LOGIC CIRCUITS 113 A In Problems 4 to 6, usenor-gates only to devise the logic systems stated. 4.Z=(A+B)·(C+ ...
Assign-03-H8152.tex 11/7/2006 12: 42 Page 114 Number and Algebra Assignment 3 This assignment covers the material contained in C ...
Geometry and trigonometry B 12 Introduction to trigonometry 12.1 Trigonometry Trigonometryis the branch of mathematics which dea ...
116 GEOMETRY AND TRIGONOMETRY (b) the value of∠QPR. [(a) 27.20 cm each (b) 45◦] A man cycles 24 km due south and then 20 km due ...
INTRODUCTION TO TRIGONOMETRY 117 B Figure 12.5 Thus sinX= 40 41 ,tanX= 40 9 = 4 4 9 , cosecX= 41 40 = 1 1 40 , secX= 41 9 = 4 5 ...
118 GEOMETRY AND TRIGONOMETRY Figure 12.7 For the right-angled triangle shown in Fig. 12.8, find: (a) sinα (b) cos[θ (c) tanθ ...
INTRODUCTION TO TRIGONOMETRY 119 B Figure 12.11 hence XZ= 20 .0 sin 23◦ 17 ′ = 20 .0(0.3953)=7.906 mm cos 23◦ 17 ′= XY 20. 0 hen ...
120 GEOMETRY AND TRIGONOMETRY (Note, ∠PRQ is also φ—alternate angles between parallel lines.) Problem 9. An electricity pylon st ...
INTRODUCTION TO TRIGONOMETRY 121 B Hence 129. 9 +x= 75 tan 20◦ = 75 0. 3640 = 206 .0m from which x= 206. 0 − 129. 9 = 76 .1m Thu ...
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