Independent contractor estimated payments when also employed not as a contractor- do my paycheck deductions covered this?

Hi,

I have been self-employed for a while now working as an independent contractor for a company, and have now gotten a full-time job where I am not paid as an independent contractor. I have been making quarterly estimated payments for my self-employment. On my W4 for the full-time job, I calculated the extra deduction (Step 2b Line 4) for having 2 jobs. Will this amount that is deducted biweekly count towards my estimated payments for my independent contractor job? From the math I've done, the extra deduction from my paycheck won't cover all of the taxes for my independent contractor job, so I would still make a small quarterly estimated payment. Just want to make sure the deductions from my paycheck will also count towards the quarterly estimated tax payments. 

This is all new to me and doesn't make much sense so I appreciate any help! Thanks!