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Prove Theorem A.5 on page 323. Prove Theorem A.6 on page 323. Prove Theorem A.7 on page 323. Run a program that tests De Moivre s formula on page 325 by comparing the values obtained from it with those obtained from the recursive definition of the Fibonacci numbers.

CHAP. 3]

(b) Edit hEx3_2.CIRi to move the leading asterisks up one position on both the transistor speci cation statement and the .MODEL statements. Execute the revised hEx3_2.CIRi and use the Probe feature of PSpice to produce the collector characteristics for the generic BJT model (QNPNG or QPNPG) as displayed by Fig. 3-5(c). Example 3.3. Apply SPICE methods to determine the CE transfer characteristics for the generic npn transistor (QNPNG). Figure 3-6(a) presents the connection method chosen for determination of the transfer characteristics. The associated netlist code follows:

A.1 A.2 A.3 The floor and ceiling functions are idempotent because they return integer values, and according to Theorem A.1 on page 319, the floor or ceiling of an integer is itself. A logarithm is an exponent. It is the exponent on the given base that produces the given value. The First Principle of Mathematical Induction ( weak induction) allows the inductive hypothesis that assumes that the proposition P(n) is true for some single value of n. The Second Principle of Mathematical Induction ( strong induction) allows the inductive hypothesis that assumes that all the propositions P(k) are true for all k less than or equal to some value of n. Use weak induction (the first principle) when the proposition P(n) can be directly related to its predecessor P(n 1). Use strong induction (the second principle) when the proposition P(n) depends upon P(k) for k < n 1. Euler s constant is the limit of the difference (1 + 1/2 + 1/3 + . . . + 1/n) lnn. Its value is approximately 0.5772. Stirling s formula is a useful method for approximating n! for large n (e.g., n > 20).

higher-level languages, 2 3 Hollerith, Herman, 8 Hopper, Grace Murray, 10 HTML (hypertext markup language), 135 137 HTTP (hypertext transport protocol), 134 135 IBM (International Business Machines Corporation), 8 imperative language, 46, 49 inheritance, 52, 78, 79, 81 82 insertion sort, 17 19 instance method, 51, 52, 78, 79 80 instance variable, 51, 52, 78, 79 80 instruction set. See machine language International Business Machines Corporation (IBM), 8 internet, 128 reference model, 129, 129 134 internet protocol (IP), 131 132 interpreter, 48 49 I/O, 40-1 direct memory access (DMA), 100 interrupt-driven, 100 management, 99 memory mapped, 101 programmed, 100 See also Java: input/output IP (internet protocol), 131 132, 133 134 ISO OSI reference model, 128, 128 129 iteration. See looping Jacquard, Joseph Marie, 5 Jacquard loom, 5, 7 Java, 47, 49, 50 51, 66 control structures, 71 77 data types, 66 70 error handling, 85 87 identifiers, 71 input/output, 87 92 interfaces, 83 84 operators, 70 variables and methods, 79 84 Java Virtual Machine (JVM), 49 JDBC, 162 165 job control language (JCL), 97 LAN (local area network), 127 128. See also network languages design properties of, 59 60 history of, 44 47, 59 syntax and semantics of, 61 64 See also compiler; interpreter; specific language

Fig. 3-6

A.1 Proof of Theorem A.1 on page 319: a. The relationships x = max{m Z | m x}, and restatements of the definitions of x and x .

Ex3_3.CIR Vbe 1 0 0V Q 2 1 0 QNPNG Vc 2 0 1V .MODEL QNPNG NPN(Is=10fA Ikf=150mA Isc=10fA Bf=150 + Br=3 Rb=1ohm Rc=1ohm Va=30V Cjc=10pF Cje=15pF) .DC Vbe 0V 2V 0.01V Vc 0V 2V 0.2V .PROBE .END

APPENDIX]

Execution of hEx3_3.CIRi and use of the Probe feature of PSpice yields the desired transfer characteristics displayed by Fig. 3-6(b). Example 3.4. Using SPICE methods, determine the CB collector characteristics for the generic pnp transistor (QPNPG). Figure 3-7(a) shows the circuit for use in the determination. The netlist code below describes that circuit.