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2 二进制补码之和

[英]Sum of 2 two's complement binary number

原文 2021-11-09 17:06:06 3 1 math/ binary/ addition/ twos-complement

I am familiar with two's complement when performing addition in 4 bits, then I am confused when I face the question below我在执行 4 位加法时熟悉二进制补码，然后当我面对以下问题时感到困惑

** Find the sum of the 2 two's complement binary number 010111 and 110101 in 8 bit output** ** 在 8 位输出中找到 2 个二进制补码二进制数 010111 和 110101 的和**

Below is my attempt, but I am in a dilemma, should I以下是我的尝试，但我处于两难境地，我应该

(1) discard the carry, then add two 0, so the answer is 00001100, which is 12 in decimal (1) 丢弃进位，然后加两个0，所以答案是00001100，也就是十进制的12

Thank you !谢谢！

(2) just add 1 in the beginning, so it the answer is 11001100, which is 204 in decimal (2) 开头加1，所以答案是11001100，也就是十进制的204

1 个解决方案

For the Twos Complement in 8 bit you have to invert ALL 8 bits of the number对于 8 位的二进制补码，您必须反转数字的所有 8 位

As far as i know the ones complement and twos complement operate on the absolute value so:据我所知，二进制补码和二进制补码对绝对值进行运算，因此：

The Binary Number 010111 is represented in 8 bits with 00010111二进制数 010111 用 00010111 用 8 位表示

C_1(00010111) = 00010111 xor 11111111 = 11101000 C_1(00010111) = 00010111 异或 11111111 = 11101000

C_2(00010111) = C_1 + 1 = 00010111 + 1 = 00011000 C_2(00010111) = C_1 + 1 = 00010111 + 1 = 00011000

The Binary Number 110101 is represented in 8 bits -> 00110101二进制数 110101 用 8 位表示 -> 00110101

C_1(00110101) = 00110101 xor 11111111 = 11001010 C_1(00110101) = 00110101 异或 11111111 = 11001010

C_2(00010111) = C_1 + 1 = 11001010 + 1 = 11001011 C_2(00010111) = C_1 + 1 = 11001010 + 1 = 11001011

Now add the two twos-complements: C_2(00010111) + C_2(00010111) = 00011000 + 11001011 = 11100011现在添加两个补码：C_2(00010111) + C_2(00010111) = 00011000 + 11001011 = 11100011

Pls correct me if messed something up with sign bits (I just took the binary numbers as is in 8 bit)...如果用符号位弄乱了一些东西，请纠正我（我只是按照 8 位的原样取二进制数）...