The cup is a volume measurement unit used in cooking. Therefore, it is mainly used in serving sizes and for cooking purposes. Traditionally in the US, it is something between 200 and 250ml and that can be said to be about ¼ a litre or less when compared with the metric system of volume measurement. Therefore, there is a standard cup for measuring volumes.
A gallon is about 4 litres and therefore, half a gallon is roughly 2 litres. In that case, a half gallon will be (2/ ¼ ) cups = 8 cups.