Date issues

I have 2 issues I am struggling with
1. In column A I have a person date of birth 1971/06/01. In column B I have "=today()", which shows 2009/06/01. In column C I have "=B1-A1", with format "yy" to display the age, but 1 year less is shown. Only from tomorrow is the age correct. How do I fix the function in Colomn C

2. The same file. If you change the format to "ddmm", both column A and B will show 0106, and in column D "=IF(A1=B1,1,0)", a "0" is displayed. How do I fix to show "1" in column D

Thanks

Use DATEDIF

=DATEDIF(A1,B1,"y") or =DATEDIF(A1,TODAY(),"y")

see: http://www.cpearson.com/excel/datedif.htm