Can I create a cell with a formula that will change it's cell value based off another cells value? Excel 2010 or 2013

For example:

Can I have cells setup so that,

if the number 1 is typed into cell A1 it will return the value from cell B1, "Cat"

if the number 2 is typed into the cell A2 it will return the value from Cell B2, "Dog"

if the number 1 is typed into the cell A3 it will return the value from Cell B1, "Cat"

if the number 3 is typed into the cell A4 it will return the value from Cell B3, "Fish"

etc, etc.

I need to be able to paste a huge list of numbers into a column and have them change based off what number was input.