@Deepa
Sounds like you are trying to "cookie cut" a section of the raster using your county feature class boundary.
You are correct that you can use Extract By Mask . Additionally you could use Clip Raster and specify the bounding geometry.
Note that in this case the output raster is a minimum bounding rectangle of the mask (county features) by default. You can optionally control the analysis extent using the extent environment setting.
Every cell location in a raster has a value assigned to it . When information is unavailable for a cell location, the location will be assigned as NoData. Note that NoData and 0 are not the same—0 is a valid numerical value
You can convert to ascii using the Raster to Ascii conversion tool.
Good luck