Question

我在这里缺少什么？我对手写的二进制到十进制转换比较新，而且我无法弄清楚为什么，至少对我来说，1110和1111似乎都等于15，但我知道1110 = 14。

Binary = 1110
n =      3210
calc = (1*2)^3 = 8
       (1*2)^2 = 4
       (1*2)^1 = 2
       (0*2)^0 = 1
       = 15

Binary = 1111
n =      3210
calc = (1*2)^3 = 8
       (1*2)^2 = 4
       (1*2)^1 = 2
       (1*2)^0 = 1
       = 15

Answer 1

我认为您的混淆在于您的公式不正确，(An*2)^n不是An*(2^n)（PEMDAS）：

1110
1 * 2^3 = 8
1 * 2^2 = 4
1 * 2^1 = 2
0 * 2^0 = 0
         --- 
          14

1111
1 * 2^3 = 8
1 * 2^2 = 4
1 * 2^1 = 2
1 * 2^0 = 1 
         ---
          15

Answer 2

您的公式（在您的问题标题中）只有错误的优先顺序。它不是(An x 2)^n…(A0 x 2)^0，而是An x (2^n)…A0 x (2^0)。

Binary = 1110
n =      3210
calc = 1*2^3 = 1*8 = 8
       1*2^2 = 1*4 = 4
       1*2^1 = 1*2 = 2
       0*2^0 = 0*1 = 0
       = 14

Binary = 1111
n =      3210
calc = 1*2^3 = 1*8 = 8
       1*2^2 = 1*4 = 4
       1*2^1 = 1*2 = 2
       1*2^0 = 1*1 = 1
       = 15

二进制转换 - 使用（An x 2）^ n ...（A0 x 2）^ 0

2 个答案: