Taxable income for retirees

My wife and are are both retired and over 65 years old. We each receive our Social Security payments as our sole income. We have no other income sources. We would like to withdraw some of our retirement savings from our traditional IRA’s. I know that withdrawals from traditional IRA’s are treated as ordinary income for tax purposes. Are we allowed withdrawals up to the standard deduction limit before we owe any taxes? Both my wife and I are currently not subject to the mandatory distribution.