reflect add one 0100 0111 → 1011 1000 → 1011 1001

It is always a good idea to check your results:

```  11111 111
0100 0111
+ 1011 1001
0000 0000
```

# Two's Complement Integers

What is the two's complement of zero?

```      zero =  0000 0000
reflect =  1111 1111
```

Using the algorithm with the representation for zero results in the representation for zero. This is good. In mathematics, "minus zero" is the same thing as "zero". It is good to have just one representation of zero. Recall that with the sign-magnitude method of representing integers there where both "plus" and "minus" zero.

What integers can be represented in 8-bit two's complement? Two's complement represents both positive and negative integers. So one way to answer this question is to start with zero, check that it can be represented, then check one, then check minus one, then check two, then check minus two ... Let's skip most of those steps and check 12710:

```       127 =  0111 1111            check:   0111 1111
reflect =  1000 0000                     1000 0001
add one =  1000 0001                     0000 0000

-127 =  1000 0001
```

### QUESTION 19:

Now try to compute the negative of 128ten.

```       128  =  1000 0000

reflect  =