I am new to cryptography. I am looking to understand how to answer this question from my class:
Find below the S-box of AES. Given the input 01010011 in binary, calculate the output.
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An AES S-box is nothing else than a permutation. You give it a input, and it give you the corresponding output.
Here the S-box is represented by a 2D array. If your input is $01010011$, you have to get it's hexadecimal representation : $0x53$ (because an hexadecimal is represented by four bits, $0101 = 5$ and $0011 = 3$).
Now you only have to get the corresponding output of the Sbox ($5$ is the left nibble, en $3$ the right nibble).
Since $0011$ is your right nibble and $0101$ is your left nibble, row 5 and column 3 give the output of 50 (hex) or $01010000$ in binary.