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Carry can be a difficult concept to understand. Hopefully this page will help.
If you went to school in an English-speaking country, you might be familiar with the word in this context but it is still confusing. If you speak another language you probably have a word for it too.
For example, when adding two numbers:
27 + 35 ----
You can do this easily but consider it at a methodical level. We add seven to five to get twelve; we write a 2 and "carry" the 1 to the next column:
27 + 35 ---- 2 1
Next we add two, three and the "carried" one to get six and hence the result:
27 + 35 ---- 62 1
That's great. Now let's do it in binary.
%01 + %01 ----- %10 1
There: we "carried" a 1 from bit 0 into bit 1 of the result. For a more realistic case:
%11111111 + %00000001 ----------- %100000000
The problem here is that the result is bigger than 8 bits; so, we cut off the 1 at the start and store that in the carry bit. This tells us that there was a "carry out" of the high bit of the result and a "carry in" to the Carry flag.
You may remember that at school there was something similar for subtraction; sometimes, you need to "borrow" from the next digit to have enough to make a positive result. Example:
43 - 15 ----
You can't subtract five from three, so you "borrow" one from the next column; thirteen minus five is eight:
1 3 3 - 1 5 ------ 8
The next digit is then found by subtracting one from three and it is finished.
1 3 3 - 1 5 ----- 2 8
In binary, much the same happens:
%110 - %101 ------ %001
As we get up to eight bits, sometimes we need to "borrow" from an imaginary ninth column:
%00000000 %100000000 - %10000000 - %010000000 ----------- ------------ ???????? %010000000
In these cases, we just "borrow" whatever we need to make it possible to get a result; the carry bit can tell whether anything was "borrowed" from the imaginary ninth bit. You can also describe it as a "carry in" to the high bit from the Carry flag.
Whenever an addition would make a result bigger then eight bits, the carry flag will become
1; you can use this (with instructions like
adc) to add that "carry out" onto another byte so you can effectively chain bytes together to make large numbers.
When a subtraction would make a negative number, the carry flag will become
1 and the result will instead be that negative number plus 256 (in signed notation; in two's complement notation it is a negative number).
When using the carry/no carry conditions with decrements in Z80 code, you need to remember that it becomes
1 on the transition from 0 to -1, which is one step later than the transition from 1 to 0 which triggers the zero condition. This can be useful or equally a tricky bug to discover.