Process the img1 using the img2 which contained with only 0 and 1 to keep the raster corresponding 1 and erase the raster corresponding 0

Question

How can I use an image with only 0 and 1 to process another image, so that the original image value corresponding to the 0 value area becomes 0, and the value corresponding to 1 is preserved? Is there any tools in ArcGIS to handle? I used the Extract by Mask tool in ArcGIS, and I found that the tool can not recognized the areas outside the image and makes no difference to the areas inside the image, but the two image have the same size. I want to batch extraction because I have hundreds of images to process.