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Chap1 Digital Systems and Binary Numbers

电子电路作用：处理信息、能量转换

Note

  • Structure
  • hierarchical design
  • limited complexity at each level
  • reusable building blocks
  • Interface
  • key elements of system engineering
  • isolate technologies, allow evolution
  • major abstraction mechanism
  • Design
  • minimal mechanism, maximal function
  • reliable in a wide range of environments
  • accommodates future technical improvements

Note

  • 数制：
  • 码制：用不同数码表示不同事物的规则
  • 数字电路中采用二进制
  • 表示数量时称二进制
  • 表示事物时称二值逻辑

Complements of numbers

Dimished radix complement: Given a number N in base r having n digits, the (r-1)'s complement of N, i.e., its dimished radix complements, is defined as (r^n - 1) - N

Radix complement: The r's complement of an n-digit number N in base r id defined as r^n - N

Signed Binary Numbers

ways to represent negetive numbers: signed-magnitude & signed-complement

Example

  • signed-magnitude: 10001001
  • signed-1's-complement: 11110110
  • signed-2's-complement: 11110111

!!! note 原码、反码、补码 - 正数的补码和原码相同 - 负数的补码 = 数值位诸位求反 + 1

Note

  • 补码的扩展：前置位全为符号数
  • 小数的补码：取补时末尾 +1，不是数值 +1

Binary Codes

Note

Binary-Coded Decimal(BCD, 8421): each group of 4 bits representing one decimal digit

Decimal Codes: BCD8421、2421、Excess-3、84-2-1、6311(631-1)

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Note

American Standard Code for Information Interchange(ASCII): use seven bits to code 128 characters

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Note

Error-Detecting Code: a parity bit is an extra bit included with a message to make the total number of 1's either even or odd

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Binary Storage and Registers

Binary Logic

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