Higher Engineering Mathematics

82 NUMBER AND ALGEBRA [Checking, using the quadratic formula: x= −(−6)± √ [(−6)^2 −(4)(4)(−7)] (2)(4) = 6 ± 12. 166 8 =−0.771 an ...

SOLVING EQUATIONS BY ITERATIVE METHODS 83 A Sincex 4 andx 5 are the same when expressed to the required degree of accuracy, then ...

84 NUMBER AND ALGEBRA required root is1.05, correct to 3 significant figures. Checking, using the quadratic equation formula, x= ...

SOLVING EQUATIONS BY ITERATIVE METHODS 85 A Thus, r 2 = 3 − 19. 35 − 463. 7 = 3 + 0. 042 = 3. 042 = 3 .04, correct to 3 signific ...

Number and Algebra 10 Computer numbering systems 10.1 Binary numbers The system of numbers in everyday use is thedenary ordecima ...

COMPUTER NUMBERING SYSTEMS 87 A 10.3 Conversion of denary to binary An integer denary number can be converted to a cor- respondi ...

88 NUMBER AND ALGEBRA Now try the following exercise. Exercise 43 Further problems on conver- sion of denary to binary numbers I ...

COMPUTER NUMBERING SYSTEMS 89 A Dividing repeatedly by 8, and noting the remainder gives: 7 2 0 2 8 3 714 Remainder 8 464 2 8 5 ...

90 NUMBER AND ALGEBRA Convert the binary numbers given to denary numbers via octal. (a) 111.011 1 (b) 101 001.01 (c) 1 110 011 ...

COMPUTER NUMBERING SYSTEMS 91 A (b) BD 16 =B× 161 +D× 160 = 11 × 16 + 13 × 1 = 176 + 13 = 189 ThusBD 16 = (^18910) Problem 13. C ...

92 NUMBER AND ALGEBRA is assigned to each group. For example, the binary number 1110011110101001 is initially grouped in fours a ...

COMPUTER NUMBERING SYSTEMS 93 A 5. 5410 [36 16 ]6. 20010 [C8 16 ] 7. 9110 [5B 16 ]8. 23810 [EE 16 ] In Problems 9 to 12, convert ...

Number and Algebra 11 Boolean algebra and logic circuits 11.1 Boolean algebra and switching circuits Atwo-state deviceis one who ...

BOOLEAN ALGEBRA AND LOGIC CIRCUITS 95 A Figure 11.3 Figure 11.4 To achieve a given output, it is often neces- sary to use combin ...

96 NUMBER AND ALGEBRA Problem 2. Derive the Boolean expression and construct a truth table for the switching circuit shown in Fi ...

BOOLEAN ALGEBRA AND LOGIC CIRCUITS 97 A Problem 4. Derive the Boolean expression and construct the switching circuit for the tru ...

98 NUMBER AND ALGEBRA Figure 11.10 The circuit shown in Fig. 11.11 [ A·B·(B·C+B·C+A·B); see Table 11.6, col. 6 ] Figure 11.11 ...

BOOLEAN ALGEBRA AND LOGIC CIRCUITS 99 A Figure 11.17 Table 11.7, column 6 [ A·B·C+A·B·C+A·B·C +A·B·C; see Fig. 11.18 ] Figure ...

100 NUMBER AND ALGEBRA Problem 7. Simplify F·G·H+F·G·H+F·G·H With reference to Table 11.8: Reference F·G·H+F·G·H+F·G·H =F·G·(H+H ...

BOOLEAN ALGEBRA AND LOGIC CIRCUITS 101 A 11.4 De Morgan’s laws De Morgan’s laws may be used to simplifynot- functions having two ...