So 0 I owe no taxes, 1 I owe taes?
0 = more withholding now = pay less or receive refund on April 15 next year.
1 (or more) = less withholding now = higher net paycheck = chance of owing more next April 15.
Generally, true. However, it depends on outside income - including passbook savings accounts, etc. If you are a coupon clipper or a great poker player, you could still owe taxes with "0" deductions.
If you declare 0, it is very unlikely you will owe anything, and more than likely you will get money back, because you WILL declare 1 on your tax return at the end of the year.