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I tried:
sage: E = EllipticCurve(GF(97), [2,3])
sage: P = E.random_point()
sage: P
(22 : 5 : 1)
sage: x, y, z = P
sage: x, y, z
(22, 5, 1)
sage: bin(x), bin(y), bin(z)
('0b10110', '0b101', '0b1')
sage: ZZ(x).binary(), ZZ(y).binary(), ZZ(z).binary()
('10110', '101', '1')
Note that since $97$ is not a power of two, there is no structural path from the random point (components) to the binaries... It is just a way to "(en)code" the data.
