New Employer Mid-Year, New 401k, Question about Contribution Limits and Responsibility

My previous employer just did a general layoff and my position was on the list. Up to this point I'd contributed $7,455 to their 401k plan, not including match. I'll be starting with a new firm soon, which will mean a new 401k plan which I'll roll my old account into.

I get the feeling that my annual contribution limit of $24,500 applies no matter how many 401k's I'm contributing to which leads to my question. I like to max out when I can, will the new plan know what I've contributed to my former employer's plan and stop taking new contributions once the max is reached or for the first year do I need to do the math myself because this year's contributions will be spread across two separately managed plans?

Googling is giving me mixed messages on this. Thank you for any help.