-1 or other negative numbers are normally implemented using two's complement. So to represent -1 in two's complement form, invert the bits and add 1:
So 1 is 001
Inverting the bits gives
Adding 1 gives
Remember this is just a conventional way of representing a negative number in a digital system so that arithmetic can be done and work out ok.
So adding -1 and 1 gives -1 + 1 = 0
or in binary 111 + 001 = 1000.
Because only three bits are used, the 4th bit would be "unseen" by the digital system and the result in this example would be interpreted as 000 or zero.
You can more about two's compliment here: