This might sound a bit...but hang with me please...
Are the symbols "0" and "1" also definable as pixel values on a large screen? If so, what is a pixel? It it further composed of smaller micro pixels? Or is it pixels all the way down?
What I'm saying is that a binary computer cannot write "A" to its memory any more than you can write a green patch to a black-and white monitor's pixel.
Sure, there are various work around...you could dither, and make some bit patterns represent red, green, etc...or you could put a picture of an apple onscreen with an arrow pointing to it which said "this is red".
And just like a color monitor can display more information than a black and while monitor can, the programs of a Turing machine with more symbols can express more information in smaller strings than a binary turing machine can.