Chapter 2: Representing and Manipulating Information

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Representing and Manipulating Information

Aside How to read this chapter

2.1 Information Storage

Aside The evolution of the C programming language

New to C? The role of pointers in C

2.1.1 Hexadecimal Notation

Practice Problem 2.1 (solution page 179)

Practice Problem 2.2 (solution page 179)

Practice Problem 2.3 (solution page 180)

Aside Converting between decimal and hexadecimal

Practice Problem 2.4 (solution page 180)

2.1.2 Data Sizes

2.1.3 Addressing and Byte Ordering

Aside Origin of “endian”

New to C? Naming data types with typedef

New to C? Formatted printing with printf

New to C? Pointers and arrays

New to C? Pointer creation and dereferencing

Aside Generating an ASCII table

Practice Problem 2.5 (solution page 180)

Practice Problem 2.6 (solution page 181)

2.1.4 Representing Strings

Practice Problem 2.7 (solution page 181)

2.1.5 Representing Code

Aside The Unicode standard for text encoding

2.1.6 Introduction to Boolean Algebra

Practice Problem 2.8 (solution page 181)

Web Aside DATA:BOOL More on Boolean algebra and Boolean rings

Practice Problem 2.9 (solution page 182)

2.1.7 Bit-Level Operations in C

Practice Problem 2.10 (solution page 182)

Practice Problem 2.11 (solution page 182)

Practice Problem 2.12 (solution page 182)

Practice Problem 2.13 (solution page 183)

2.1.8 Logical Operations in C

Practice Problem 2.14 (solution page 183)

Practice Problem 2.15 (solution page 184)

2.1.9 Shift Operations in C

Practice Problem 2.16 (solution page 184)

Aside Shifting by k, for large values of k

Aside Operator precedence issues with shift operations

2.2 Integer Representations

2.2.1 Integral Data Types

2.2.2 Unsigned Encodings

PRINCIPLE: Uniqueness of unsigned encoding

2.2.3 Two’s-Complement Encodings

PRINCIPLE: Definition of two’s-complement encoding

PRINCIPLE: Uniqueness of two’s-complement encoding

Practice Problem 2.17 (solution page 184)

Aside More on fixed-size integer types

Aside Alternative representations of signed numbers

Practice Problem 2.18 (solution page 185)

2.2.4 Conversions between Signed and Unsigned

Practice Problem 2.19 (solution page 185)

Practice Problem 2.20 (solution page 185)

2.2.5 Signed versus Unsigned in C

Practice Problem 2.21 (solution page 185)

2.2.6 Expanding the Bit Representation of a Number

Web Aside DATA:TMIN Writing TMin in C

Practice Problem 2.22 (solution page 186)

Practice Problem 2.23 (solution page 186)

2.2.7 Truncating Numbers

PRINCIPLE: Truncation of an unsigned number

DERIVATION: Truncation of an unsigned number

PRINCIPLE: Truncation of a two’s-complement number

DERIVATION: Truncation of a two’s-complement number

Practice Problem 2.24 (solution page 186)

2.2.8 Advice on Signed versus Unsigned

Practice Problem 2.25 (solution page 187)

Practice Problem 2.26 (solution page 187)

2.3 Integer Arithmetic

2.3.1 Unsigned Addition

Aside Security vulnerability in getpeername

Aside Security vulnerability in getpeername (continued)

DERIVATION: Unsigned addition

PRINCIPLE: Detecting overflow of unsigned addition

Practice Problem 2.27 (solution page 188)

PRINCIPLE: Unsigned negation

DERIVATION: Unsigned negation

Practice Problem 2.28 (solution page 188)

2.3.2 Two’s-Complement Addition

PRINCIPLE: Two’s-complement addition

DERIVATION: Two’s-complement addition

PRINCIPLE: Detecting overflow in two’s-complement addition

DERIVATION: Detecting overflow of two’s-complement addition

Practice Problem 2.29 (solution page 188)

Practice Problem 2.30 (solution page 189)

Practice Problem 2.31 (solution page 189)

Practice Problem 2.32 (solution page 189)

2.3.3 Two’s-Complement Negation

PRINCIPLE: Two’s-complement negation

DERIVATION: Two’s-complement negation

Practice Problem 2.33 (solution page 189)

Web Aside DATA:TNEG Bit-level representation of two’s-complement negation

2.3.4 Unsigned Multiplication

2.3.5 Two’s-Complement Multiplication

Practice Problem 2.34 (solution page 189)

Practice Problem 2.35 (solution page 190)

Practice Problem 2.36 (solution page 190)

Practice Problem 2.37 (solution page 191)

Aside Security vulnerability in the XDR library

2.3.6 Multiplying by Constants

PRINCIPLE: Multiplication by a power of 2

DERIVATION: Multiplication by a power of 2

PRINCIPLE: Unsigned multiplication by a power of 2

PRINCIPLE: Two’s-complement multiplication by a power of 2

Practice Problem 2.38 (solution page 191)

Practice Problem 2.39 (solution page 192)

Practice Problem 2.40 (solution page 192)

Practice Problem 2.41 (solution page 192)

2.3.7 Dividing by Powers of 2

PRINCIPLE: Unsigned division by a power of 2

DERIVATION: Unsigned division by a power of 2

PRINCIPLE: Two’s-complement division by a power of 2, rounding up

DERIVATION: Two’s-complement division by a power of 2, rounding up

Practice Problem 2.42 (solution page 192)

Practice Problem 2.43 (solution page 193)

2.3.8 Final Thoughts on Integer Arithmetic

Practice Problem 2.44 (solution page 193)

2.4 Floating Point

Aside The IEEE

2.4.1 Fractional Binary Numbers

Practice Problem 2.45 (solution page 193)

Practice Problem 2.46 (solution page 194)

2.4.2 IEEE Floating-Point Representation

Case 1: Normalized Values

Aside Why set the bias this way for denormalized values?

1. Normalized

2. Denormalized

3a. Infinity

3b. NaN

Case 2: Denormalized Values

Case 3: Special Values

2.4.3 Example Numbers

Practice Problem 2.47 (solution page 194)

Practice Problem 2.48 (solution page 195)

Practice Problem 2.49 (solution page 195)

2.4.4 Rounding

Practice Problem 2.50 (solution page 195)

Practice Problem 2.51 (solution page 195)

Practice Problem 2.52 (solution page 196)

1. Format A

2. Format B

2.4.5 Floating-Point Operations

2.4.6 Floating Point in C

Practice Problem 2.53 (solution page 196)

Practice Problem 2.54 (solution page 196)

2.5 Summary

Aside Ariane 5: The high cost of floating-point overflow

Bibliographic Notes

Homework Problems

2.55 ◆

2.56 ◆

2.57 ◆

2.58 ◆◆

2.59 ◆◆

2.60 ◆◆

Bit-Level Integer Coding Rules

2.61 ◆◆

2.62 ◆◆◆

2.63 ◆◆◆

2.64 ◆

2.66

2.67

2.68 ◆◆

2.69 ◆◆◆

2.70 ◆◆

2.71 ◆

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2.74

2.75

2.76

2.77 ◆◆

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2.82 ◆

2.83 ◆◆

2.84 ◆

2.85 ◆

2.86 ◆

2.87 ◆

2.88 ◆◆

1. Format A

2. Format B

2.89 ◆

2.90

2.91 ◆

Bit-Level Floating-Point Coding Rules

2.92 ◆◆

2.94

2.95

2.96

2.97 ◆◆◆◆

Solutions to Practice Problems

Solution to Problem 2.1 (page 73)

Solution to Problem 2.2 (page 73)

Solution to Problem 2.3 (page 74)

Solution to Problem 2.4 (page 75)

Solution to Problem 2.5 (page 84)

Solution to Problem 2.6 (page 85)

Solution to Problem 2.7 (page 85)

Solution to Problem 2.8 (page 87)

Solution to Problem 2.9 (page 89)

Solution to Problem 2.10 (page 90)

Solution to Problem 2.11 (page 91)

Solution to Problem 2.12 (page 91)

Solution to Problem 2.13 (page 92)

Solution to Problem 2.14 (page 93)

Solution to Problem 2.15 (page 93)

Solution to Problem 2.16 (page 94)

Solution to Problem 2.17 (page 101)

Solution to Problem 2.18 (page 105)

Solution to Problem 2.19 (page 107)

Solution to Problem 2.20 (page 109)

Solution to Problem 2.21 (page 112)

Solution to Problem 2.22 (page 115)

Solution to Problem 2.23 (page 116)

Solution to Problem 2.24 (page 118)

Solution to Problem 2.25 (page 119)

Solution to Problem 2.26 (page 119)

Solution to Problem 2.27 (page 125)

Solution to Problem 2.28 (page 125)

Solution to Problem 2.29 (page 129)

Solution to Problem 2.30 (page 130)

Solution to Problem 2.31 (page 130)

Solution to Problem 2.32 (page 130)

Solution to Problem 2.33 (page 131)

Solution to Problem 2.34 (page 134)

Solution to Problem 2.35 (page 135)

Solution to Problem 2.36 (page 135)

Solution to Problem 2.37 (page 135)

Solution to Problem 2.38 (page 138)

Solution to Problem 2.39 (page 139)

Solution to Problem 2.40 (page 139)

Solution to Problem 2.41 (page 139)

Solution to Problem 2.42 (page 143)

Solution to Problem 2.43 (page 143)

Solution to Problem 2.44 (page 144)

Solution to Problem 2.45 (page 147)

Solution to Problem 2.46 (page 147)

Solution to Problem 2.47 (page 153)

Solution to Problem 2.48 (page 155)

Solution to Problem 2.49 (page 156)

Solution to Problem 2.50 (page 157)

Solution to Problem 2.51 (page 158)

Solution to Problem 2.52 (page 158)

Solution to Problem 2.53 (page 161)

Solution to Problem 2.54 (page 161)