二补二元加法

Question

我有一个程序，添加2，2的补码二进制数，并吐出输出。它们是从一个文件中读取的，作为第一个二进制数在两个的补码中。第二个二进制数用有偏符号表示。为了改变形式偏向于二的补语，我们翻转最左边的位。然后，我们将这两个二进制数字添加到文件中，并给出输出。我遇到的困难是理解输出。这是输出，其中第一个二进制数是在两个的补码和第二个有偏表示法。

   01000000 <- 2's complement         64
+  11000000 <- biased notation        64
-----------------------------------------------
   10000000 <- 2's complement   Overflow

   01111111 <- 2's complement        127
+  00000000 <- biased notation      -128
-----------------------------------------------
   11111111 <- 2's complement         -1

   00000011 <- 2's complement          3
+  10000111 <- biased notation         7
-----------------------------------------------
   00000110 <- 2's complement          6

   00001111 <- 2's complement         15
+  10000111 <- biased notation         7
-----------------------------------------------
   00010010 <- 2's complement         18

   10000000 <- 2's complement       -128
+  11111111 <- biased notation       127
-----------------------------------------------
   11111111 <- 2's complement         -1

   11110000 <- 2's complement        -16
+  10001000 <- biased notation         8
-----------------------------------------------
   11111000 <- 2's complement         -8

   10000001 <- 2's complement       -127
+  00000001 <- biased notation      -127
-----------------------------------------------
   00000010 <- 2's complement   Underflow

   01111111 <- 2's complement        127
+  00000000 <- biased notation      -128
-----------------------------------------------
   11111111 <- 2's complement         -1

   01110101 <- 2's complement        117
+  11010001 <- biased notation        81
-----------------------------------------------
   01000110 <- 2's complement         70

   00000000 <- 2's complement          0
+  10000000 <- biased notation         0
-----------------------------------------------
   00000000 <- 2's complement          0

   00001111 <- 2's complement         15
+  11110000 <- biased notation       112
-----------------------------------------------
   01111111 <- 2's complement        127

   00001111 <- 2's complement         15
+  10000001 <- biased notation         1
-----------------------------------------------
   00010000 <- 2's complement         16

   00000111 <- 2's complement          7
+  11110000 <- biased notation       112
-----------------------------------------------
   01110111 <- 2's complement        119

   11111111 <- 2's complement         -1
+  01111111 <- biased notation        -1
-----------------------------------------------
   10101010 <- 2's complement        -86

   00000000 <- 2's complement          0
+  10000000 <- biased notation         0
-----------------------------------------------
   00000000 <- 2's complement          0

   11111111 <- 2's complement         -1
+  11111111 <- biased notation       127
-----------------------------------------------
   00101010 <- 2's complement         42

第三个例子是3+7= 6，这是正确的吗？这似乎不对，但其他例子是正确的。类似-16 +8= -8。

所以我的问题是..。这个文件的输出正确吗？

Answer 1

看起来，每当你有3次连续携带时，它就会下降1。与下一次相同，15 + 7。它没有正确地进行携带。

  11  <- carry
 0011 = 3
+0111 = 7
 1010 = 10