I want to build something like this:
A Note 0 Yes (red) 3 No (no color/white) 1 No (no color/white) 0 Yes (red)
but I want the "yes" and "no" to be displayed as color without the word "yes" or "no".
You want conditional formatting.
Note: Blank values evaluate to zero, so if you're expecting blanks and want to ignore them, do something like this:
Select Format, select Fill, and select the colour red.
Alternatively, if you just want to highlight the cells in column A themselves, then you can simply select the cells and do Conditional Formatting > Highlight Cells Rules > Equal To... 0, then set a custom format with red fill.