How do I add cells, but only if certain criteria are met first in other cells?

I have a little problem in working this out, I can't! I can add cells & alike, but more complex working are an unknown to me.
Any help here would be greatly appreciated.
I've three cells in a row C4 with 5 in, D4 with 3 in & E4 with 1 in. I'd like to add these numbers together into a cell below E6, which is =SUM(C4:E4) which will make 9 in cell E6.
I've also three cells in a row below C4 - E4 which are C5, D5 & E5 which will only ever have ether 0 or 1 inputted into them. All these cells will only ever have data inputted into them from left to right i.e. Column C first, then Column D & lastly Column E.
What I’d like for the cells to do, is only add cells C4 - E4 from left to right, once a cell below (C5 - E5) has had a 1 inputted into it & then continue to add the cells there after normally.
Examples:
Like above if C4 had 5, D4 had 3 & E4 had 1, & the all the cells below (C5 - E5) had 1 in them, then E6 = 9.
Again, if C4 had 5, D4 had 3 & E4 had 1, but C5 had 0, D5 had 1 & E5 had 1, then E6 = 4.
Again if cells C4 - E4 are the same, but C5 had 0, D5 had 1 & E5 had 0, then E6 still = 4.
In the same aspect as above, if C4 - E4 are the same, but C5 had 1, D5 & E5 had 0, then E6 = 9.
If cells C4 - E4 are the same, but C5 - E5 all had 0, then E6 = 0.
I hope this is clear, & all comments are welcome.
Many Thanks.

Big_Botts wrote:
Hi Barry,
Just a thought, Wayne is helping me on another question I asked, do you think you could help?
https://discussions.apple.com/message/17950789#17950789
Wayne's got that one well in hand. Nothing to add there, except that you'll find the details about conditional formatting in the Numbers '09 User Guide, which can be downloaded via the Help menu in Numbers. While you're there, grab the iWork Formulas and Functions User Guide as well. Both are quite useful.
Regards,
Barry
Regards,
Barry

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> Want to add a members only site to my web site, how
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> help /
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