The subject of this book is the analysis and design of digital devices that implement computer arithmetic. The book's presentation of high-level detail, descriptions, formalisms and design principles means that it can support many research activities in this field, with an emphasis on bridging the gap between algorithm optimization and hardware implementation. The author provides a unified view linking the domains of digital design and arithmetic algorithms, based on original formalisms and hardware description languages. A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. The book is suitable for researchers and students engaged with hardware design in computer science and engineering. A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. The book is suitable for researchers and students engaged with hardware design in computer science and engineering. Computer Arithmetic 2 Contents 4 Chapter 1: The Representation of Numbers in Computing Systems 6 1.1 Information Classi?cation 6 1.2 The Representation of Fixed Point Numbers 7 1.2.1 The Representation of Fixed Point Binary Numbers 7 1.2.2 The Representation of Fixed Point Decimal Numbers 16 1.3 The Representation of Floating Point Numbers 18 Chapter 2: Functional Analysis and Synthesis of Binary and Decimal Adding and Subtracting Devices 25 2.1 Serial Adders 25 2.2 Parallel Adders and Subtracters 29 2.2.1 Binary Adders Based on Serial Carry Propagation 29 2.2.2 Decimal Adders Based on Serial Carry Propagation 35 2.2.3 Subtracters Based on Serial Carry/Borrow Propagation 39 2.2.4 Carry-Lookahead Adders 42 2.2.5 Carry-Skip Adder 50 Chapter 3: Functional Analysis and Synthesis of Binary Multiplication Devices 70 Chapter 4: Functional Analysis and Synthesis of Binary Division Devices 146 Chapter 5: Functional Analysis and Synthesis of Floating Point Arithmetic Devices 198 5.1 Characteristics of the Floating Point Operation 198 5.2 Floating Point Addition and Subtraction 211 Step 1 217 Step 2 217 Step 3 217 Step 4 218 Step 5 218 Step 6 219 Step 7 221 Step 8 222 Step 9 222 Step 10 223 A 225 B 227 B1 228 B2 231 B3 233 B3a 233 B3b 235 5.3 Floating Point Multiplication and Division 243 Appendix A: Hardware Description Elements 250 -- The subject of this book is the analysis and design of digital devices that implement computer arithmetic. The book's presentation of high-level detail, descriptions, formalisms and design principles means that it can support many research activities in this field, with an emphasis on bridging the gap between algorithm optimization and hardware implementation. The author provides a unified view linking the domains of digital design and arithmetic algorithms, based on original formalisms and hardware description languages. -- -- A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures. -- -- The book is suitable for researchers and students engaged with hardware design in computer science and engineering Front Matter....Pages I-VI The Representation of Numbers in Computing Systems....Pages 1-19 Functional Analysis and Synthesis of Binary and Decimal Adding and Subtracting Devices....Pages 21-65 Functional Analysis and Synthesis of Binary Multiplication Devices....Pages 67-142 Functional Analysis and Synthesis of Binary Division Devices....Pages 143-194 Functional Analysis and Synthesis of Floating Point Arithmetic Devices....Pages 195-246 Back Matter....Pages 247-267 Computer Arithmetic provides a complete procedure for linking the digital design and arithmetic algorithms domain, based on original formalism and hardware description languages. Readers will find gate-level designs for all matrix/combinatorial arithmetic structures.
