Chapter 5 Number Represent and Arithmetic Ciacuit 逻辑电路及其完成的算术运算 (217)

5.1 Positional Number Representation LSB 最低有效位 MSB 最高有效位 Nibble 半字节 Byte 字节 Left Shift －－ multiply Right shift －－ divider

Conversion between each other Binary Decimal 十进制 Octal 八进制 Hexadecimal 十六进制

5.2 Addition of unsigned numbers Half adder-no carry in Full adder-with carry in Ripple-carry Adder ( 行波）逐位进位 （并行加法器）

Arithmetic Circuit Adder 加法器 HA 、 FA 、 RCA 、 Multiplication 乘法器

5.3 Signed numbers Negatives numbers 负数 Sign-and-magnitude 符号－量 ’s complement 反码 ’s complement 补码

5.3.2 Addition and subtraction 1’complement add: Result: add “n” become all 1, then is negative “n” Ex: =1111, negative 3 ! carry out from the sign bit should add bake to the LSB position! Not simple

2’complement add: Result: add “n” become all 0, then is negative “n” Ex: =0000, negative 3 carry out from the sign simply ignore simple! Subtrahend 减数 Minuend 被减数

5.3.4 Radix-Complement Schemes 9’s complement 十进制反码 10’s complement 十进制补码

5.3.5 Arithmetic overflow Carry out of Sign bit XOR MSB

Price / performance ratio Speed The path that causes the longest delay is called critical path 关键路径

5.4 Fast Adder Carry-lookahead adder 超前进位加法器