Check if a number is divisible by 3

Write code to determine if a number is divisible by 3. The input to the function is a single bit, 0 or 1, and the output should be 1 if the number received so far is the binary representation of a number divisible by 3, otherwise zero.

Examples:

input  "0":       (0)  output 1
inputs "1,0,0":   (4)  output 0
inputs "1,1,0,0": (6)  output 1

This is based on an interview question. I ask for a drawing of logic gates but since this is stackoverflow I'll accept any coding language. Bonus points for a hardware implementation (verilog etc).

Part a (easy): First input is the MSB.

Part b (a little harder): First input is the LSB.

Part c (difficult): Which one is faster and smaller, (a) or (b)? (Not theoretically in the Big-O sense, but practically faster/smaller.) Now take the slower/bigger one and make it as fast/small as the faster/smaller one.