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第 3 章 Binary Math and Signed Representations

第 3 章 Binary Math and Signed Representations. Computer Organization and Design Fundamental 書籍 作者: David Tarnoff 投影片製作者:陳鍾誠. 3.1 Binary Addition. 一位元加法 ( 半加器 ). 一位元加法 ( 全加器 ). 兩個二進位數相加. 3.2 Binary Subtraction. 一位元減法. 借位. 多位元減法. 3.3 Binary Complements ( 二補數 ). 1 補數 該數與其 1 補數相加

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第 3 章 Binary Math and Signed Representations

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  1. 第 3 章 Binary Math and Signed Representations Computer Organization and Design Fundamental 書籍作者:David Tarnoff 投影片製作者:陳鍾誠

  2. 3.1 Binary Addition

  3. 一位元加法 (半加器)

  4. 一位元加法 (全加器)

  5. 兩個二進位數相加

  6. 3.2 Binary Subtraction

  7. 一位元減法 借位

  8. 多位元減法

  9. 3.3 Binary Complements (二補數) • 1 補數 • 該數與其 1補數相加 • 再加上 1

  10. 二補數的秘密

  11. 二補數加減法的例子 • 88 與 10 的二進位與二補數 • 88-10 的二補數減法過程

  12. 計算 2 補數的技巧

  13. 2 補數的補數 • In decimal, the negative of 5 is -5. If we take the negative a second time, we return to the original value, e.g., the egative of -5 is 5. Is the same true for taking the 2's complement of a 2's complement of a binary number?

  14. 3.3.3 Most Significant Bit as a Sign Indicator • A binary value with a 0 in the MSB position is considered positive and a binary value with a 1 in the MSB position is considered negative

  15. 3.3.4 Signed Magnitude (正負號位元表示法)

  16. 3.3.5 MSB and Number of Bits • Since the MSB is necessary to indicate the sign of a binary value, it is vital that we know how many bits a particular number is being represented with so we know exactly where the MSB is. • 以下位元串到底代表甚麼數字呢?

  17. 3.3.6 Issues Surrounding the Conversion of Binary Numbers • 2 補數正數轉為十進位 • 2 補數負數轉為十進位

  18. 將 2 補數轉為 10 進位的流程圖

  19. 最大最小值 • 2 補數 • 正負號位元表示法

  20. 數字系統的比較

  21. 3.4 Floating Point Binary (浮點數的二進位表示法)

  22. 指數 • 10n • 2n

  23. 「浮」點的意義

  24. 浮點數的二進位編碼方式

  25. 符點數解碼 • 請問下列32 位元浮點數代表何值 11010110101101101011000000000000

  26. 符點數編碼 • 請將下列二進位數編為浮點格式 • 0.000000110110100101 步驟 1: 步驟 2: 步驟 3:

  27. 3.5 Hexadecimal Addition (16 進位加法)

  28. 16 進位加法範例 • 請計算 3DA32 加上 4292F 的結果

  29. 3.7 Multiplication and Division by Powers of Two

  30. 用移位代替乘法 • Since a shift operation is significantly faster than a multiply or divide operation, compilers will always substitute a shift operation when a program calls for a multiply or divide by a power of two. • 但在右移時必需注意 MSB 的填入值

  31. 用移位代替乘法 (C 語言版) • 乘以 8 • 除以 16

  32. 3.8 Easy Decimal to Binary Conversion Trick • 將 15610 轉為二進位 • 所以 15610 的 2 進位為 10011100

  33. 3.9 Arithmetic Overflow (溢位) • 20010 = 1 1 0 0 1 0 0 0 • 17510 = 1 0 1 0 1 1 1 1 • 20010 + 17510 溢位

  34. 溢位範例 2

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