Subtraction in direct code?

Question

Informatics

Hello! Faced a problem.
There is a number 4 -> 0100 (in direct code)
There is a number 7 -> 0111 (in direct code)
When I try to get the difference 4 - 7, I get 0X11 as a result, where X is some value that I cannot get , because I cannot "take" 1 from the next category. How to solve this problem?

Answer 1

It is better to subtract in the reverse code, through addition. Or subtract the smaller from the larger.
But if you so desire, you can subtract until the digits run out.
00000100
-
00000111
=
*1111101
But here's the problem, the last digit (where I have *) should actually be -1. there is simply no other place to borrow from.
If we do this borrowing, we get X=11111101 and -1 in the next, non-existent bit.
This is actually already a number in the reverse code! If we take a bit NOT and add 1, then we get 0011 = 3, as we should have. After all, the number itself is -3.
But why is it so? Your number is actually X - 2^8 (because the 1 is in the next non-existent digit).
Or - (2^8-X). Bitwise NOT. it's just a subtraction from 111...111. Those. ~X=(2^8-1) -X.
Ostuda 2^8-X = ~X+1.
Those. your number is actually ~X+1 modulo.