[英]How to represent a negative number with a fraction in 2's complement?
So I want to represent the number -12.5
. 所以我想代表
-12.5
的数字。 So 12.5 equals to: 所以12.5等于:
001100.100
If I don't calculate the fraction then it's simple, -12
is: 如果我不计算分数那么它很简单,
-12
是:
110100
But what is -12.5? 但是什么是-12.5? is it
110100.100
? 是
110100.100
? How can I calculate this negative fraction? 我该如何计算这个负分数?
With decimal number systems, each number position (or column) represents (reading a number from right to left): units (which is 10^0), tens (ie 10^1),hundreds (ie 10^2), etc. 对于十进制数字系统,每个数字位置(或列)表示(从右到左读取数字):单位(10 ^ 0),十(即10 ^ 1),数百(即10 ^ 2)等。
With unsigned binary numbers, the base is 2, thus each position becomes (again, reading from right to left): 1 (ie 2^0) ,2 (ie 2^1), 4 (ie 2^2), etc. 对于无符号二进制数,基数为2,因此每个位置变为(再次,从右到左读取):1(即2 ^ 0),2(即2 ^ 1),4(即2 ^ 2)等。
For example 例如
2^2 (4), 2^1 (2), 2^0 (1).
In signed twos-complement the most significant bit (MSB) becomes negative. 在带符号的二进制补码中,最高有效位(MSB)变为负数。 Therefore it represent the number sign: '1' for a negative number and '0' for a positive number.
因此它代表数字符号:负数为“1”,正数为“0”。
For a three bit number the rows would hold these values: 对于三位数,行将保存这些值:
-4, 2, 1
0 0 1 => 1
1 0 0 => -4
1 0 1 => -4 + 1 = -3
The value of the bits held by a fixed-point (fractional) system is unchanged. 由定点(分数)系统保持的位的值不变。 Column values follow the same pattern as before, base (2) to a power, but with power going negative:
列值遵循与之前相同的模式,基数(2)为幂,但功率为负:
2^2 (4), 2^1 (2), 2^0 (1) . 2^-1 (0.5), 2^-2 (0.25), 2^-3 (0.125)
-1 will always be 111.000
-1将始终为
111.000
-0.5 add 0.5 to it: 111.100
-0.5加0.5:
111.100
In your case 110100.10
is equal to -32+16+4+0.5 = -11.5. 在你的情况下,
110100.10
等于-32 + 16 + 4 + 0.5 = -11.5。 What you did was create -12 then add 0.5 rather than subtract 0.5. 你做的是创建-12然后添加0.5而不是减去0.5。
What you actually want is -32+16+2+1+0.5 = -12.5 = 110011.1
你真正想要的是-32 + 16 + 2 + 1 + 0.5 = -12.5 =
110011.1
you can double the number again and again until it's negative integer or reaches a defined limit and then set the decimal point correspondingly. 你可以反复加倍数,直到它是负整数或达到一个定义的限制,然后相应地设置小数点。
-25 is 11100111, so -12.5 is 1110011.1 -25是11100111,所以-12.5是1110011.1
So;U want to represent -12.5 in 2's complement representation 所以;你想在2的补码表示中表示-12.5
12.5:->> 01100.1
12.5: - >> 01100.1
2's complement of (01100.1):->>10011.1
(01100.1)的2的补码: - >> 10011.1
verify the ans by checking the weighted code property of 2's complement representation(MSB weight is -ve). 通过检查2的补码表示的加权代码属性来验证ans(MSB权重是-ve)。 we will get -16+3+.5=-12.5
我们得到-16 + 3 + .5 = -12.5
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