Why can't we use -1 in digital electronics?

Answer

-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

110

Adding 1 gives

111

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:

https://en.wikipedia.org/wiki/Two%27s_complement

Updated on February 19, 2018

Original Article:

By Eugene Brennan