user: I need to perform a series of binary number additions: add 0011 with 1100, 1010 with 0101, 1111 with 0000, and 0001 with 1110. Let me know the results for each pair, please.

Available functions:
name: add_binary_numbers
description: Adds two binary numbers.
parameters: type: dict
properties: a: type: string
description: The first binary number.
b: type: string
description: The second binary number.
required: a
b