Page 1 2014/10/20 cpeg323-08F\Topic3-05F 1 Topic 3 Number Representations and Computer Arithmetics Introduction to Computer Systems Engineering (CPEG 323) Page 2 2014/10/20 cpeg323-08F\Topic3-05F 1 Topic 3 Number Representations and Computer Arithmetics Introduction to Computer Systems Engineering (CPEG 323) 2014/10/20 cpeg323-08F\Topic3-05F 2 Outline Introduction Number representation and 2’s complement ALU design Integer multiplication/division Real Numbers Page 3 2014/10/20 cpeg323-08F\Topic3-05F 1 Topic 3 Number Representations and Computer Arithmetics Introduction to Computer Systems Engineering (CPEG 323) 2014/10/20 cpeg323-08F\Topic3-05F 2 Outline Introduction Number representation and 2’s complement ALU design Integer multiplication/division Real Numbers 2014/10/20 cpeg323-08F\Topic3-05F 3 Recap Review ? Steps in executing an instruction? Decoded opcode 32 result 32 a 32 b ALU What's up ahead: ? Number representation ? Arithmetic algorithms ? Logic implementation ? Instructions ? Fields of an instruction? ? Performance? ? Base of the operands? ALU Page 4 2014/10/20 cpeg323-08F\Topic3-05F 1 Topic 3 Number Representations and Computer Arithmetics Introduction to Computer Systems Engineering (CPEG 323) 2014/10/20 cpeg323-08F\Topic3-05F 2 Outline Introduction Number representation and 2’s complement ALU design Integer multiplication/division Real Numbers 2014/10/20 cpeg323-08F\Topic3-05F 3 Recap Review ? Steps in executing an instruction? Decoded opcode 32 result 32 a 32 b ALU What's up ahead: ? Number representation ? Arithmetic algorithms ? Logic implementation ? Instructions ? Fields of an instruction? ? Performance? ? Base of the operands? ALU 2014/10/20 cpeg323-08F\Topic3-05F 4 Reading Up to now, you should have read (or are reading) ? Patterson and Hennessy, chapters 1-2 and appendix A New material ? Patterson and Hennessy, chapter 3 Page 5 2014/10/20 cpeg323-08F\Topic3-05F 1 Topic 3 Number Representations and Computer Arithmetics Introduction to Computer Systems Engineering (CPEG 323) 2014/10/20 cpeg323-08F\Topic3-05F 2 Outline Introduction Number representation and 2’s complement ALU design Integer multiplication/division Real Numbers 2014/10/20 cpeg323-08F\Topic3-05F 3 Recap Review ? Steps in executing an instruction? Decoded opcode 32 result 32 a 32 b ALU What's up ahead: ? Number representation ? Arithmetic algorithms ? Logic implementation ? Instructions ? Fields of an instruction? ? Performance? ? Base of the operands? ALU 2014/10/20 cpeg323-08F\Topic3-05F 4 Reading Up to now, you should have read (or are reading) ? Patterson and Hennessy, chapters 1-2 and appendix A New material ? Patterson and Hennessy, chapter 3 2014/10/20 cpeg323-08F\Topic3-05F 5 Numbers Representation It may get complicated: ? How to represent negative numbers? ? What is the range of numbers? ? What if a number is out of the range? ? How about rational and irrational numbers? ? How does hardware add/sub/div/mul these numbers?Read More

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