  The full one sided shift space over finite symbols is approximated by an
increasing sequence of finite subsets of the space. The Laplacian on the space
is then defined as a renormalised limit of the difference operators defined on
these subsets. In this work, we determine the spectrum of these difference
operators completely, using the method of spectral decimation. Further, we
prove that under certain conditions, the renormalised eigenvalues of the
difference operators converge to an eigenvalue of the Laplacian.
