PLC mathematical instruction

I am having a problem fully understanding the mathematical instructions in PLC. why must there is a Clear Carry(CLC) when performing mathematical instruction
thanks

Which type of PLC are you talking about?

Since you don't specify the PLC I will have to answer generically.

The Carry flag is used to hold the one bit over-flow of a mathematical instruction. Some instructions can be grouped so that the Carry status of a previous instruction ins used as one of the inputs to a following instruction.

For example, a multi-digit add may add the lowest two digits of each number, possibly affecting the Carry flag, then adding the second digit of each, including the possible carry flag from the previous instruction. But the addition of the very first digits would not expect a valid Carry flag so it would be cleared before that first addition.

Similarly a shift register, as you mentioned in a previous post, may shift the highest bit into the carry flag. A following shift instruction may shift that carry flag into its lowest bit. But the very first shift may only want a zero to be shifted into the lowest bit so a Clear of the Carry may be needed before executing the first shift. On the other hand the process may need a 'one' to be shifted in so it may 'Set' the Carry flag before performing the shift.