如何将十进制数转换为 8 位有符号二进制数？

Question

Say I need to convert the decimal -125 to a signed 8-bit integer, how do I do this?

I'm a computing student and I'm struggling how to figure it out. I understand the basics of converting it to base 2 but I can't get the answer.

Thanks

Answer 1

A signed 8-bit integer reserves its highest order bit for the sign. 1 indicates the number is negative, 0 indicates the number is positive. Let's start there.

The number you're trying to convert is -125 , so the first bit should be 1 .

1XXX XXXX

For the next seven bits, we are going to see how many times the number they represent goes into the number we are trying to convert.

The second bit of our number represents 2^6 or 64 . We ask how many times 64 can go into 125 and find that the answer is 1.953125 .

We cannot represent this number as a 1 or a 0 , but we can think about it like this:

64 goes into 125 one time with a remainder of 0.953125 times (or 61)

Let's count the one time in our second bit and use the remainder 61 as our new number.

11XX XXXX

Next is the third bit which represents 2^5 or 32 . How many times can 32 go into 61 ? The answer is not a whole number, but 1.90625 so we follow the logic from the previous step again: using 1 as our third digit and 29 as our new number.

111X XXXX

The fourth bit represents 2^4 or 16 which goes into 29 once with a remainder of 13 .

1111 XXXX

The fifth bit represents 2^3 or 8 which goes into 13 once with a remainder of 5 .

1111 1XXX

The sixth bit represents 2^2 or 4 which goes into 5 once with a remainder of 1 .

1111 11XX

The seventh bit represents 2^1 or 2 which goes into 1 zero times.

1111 110X

The eighth and final bit represents 2^0 or 1 which goes into 1 once.

1111 1101

Thus our 8-bit signed representation of -125 is 11111101 .