Defining a variable inside `exec(...)` works in the global scope, but in the local scope

Question

Consider the following code which uses Python's built-in funciton exec.

exec('a = 1')
print(a) # prints just fine

def foo():
    exec('b = 2')
    print(b) # NameError: name 'b' is not defined

foo()

When exec is used in the global context to define a variable a, the variable is available (e.g. print(a) works); however, when exec is used to define a variable, b inside a function, the variable is not available (e.g. print(b) causes a NameError).

What's going on? Do I have to pass in the function's local context to exec?