  We study a string bit Hamiltonian whose continuum limit describes
anti-periodic (AP) anti-commuting worldsheet fields. We calculate the amplitude
for transitions between an AP spin chain and a periodic (P) one in the
continuum limit, M-> infinity where M is the bit number of either chain. We
also numerically evaluate the corresponding amplitudes at increasing finite M
to assess the convergence rate to the continuum. We then give the overlap
equations for the transition AP+AP->AP, and numerically solve them for
increasing $M$ values at a fixed value of x=K/M, where M is the bit number of
the large chain and K is the bit number of one of the smaller chains. For this
case, in contrast to the situation with an even number of AP chains, there is
an obstacle to directly finding the continuum limit analytically. We suggest an
indirect analytic approach to this problem: using the AP->P transition followed
by a P->AP+AP transition, each of which has a relatively simple analytic
continuum limit. We also show how bosonization of the fermion fields enables an
analytic recursive evaluation of the AP$+$AP$\to$AP amplitudes.
