We study f0; 1g and f􀀀1; 1g polynomials f(z), called
Newman and Littlewood polynomials, that have a prescribed num-
ber N(f) of zeros in the open unit disk D = fz 2 C : jzj < 1g.
For every pair (k; n) 2 N2, where n 7 and k 2 [3; n 􀀀 3], we
prove that it is possible to nd a f0; 1g{polynomial f(z) of de-
gree deg f = n with non{zero constant term f(0) 6= 0, such that
N(f) = k and f(z) 6= 0 on the unit circle @D. On the way to
this goal, we answer a question of D. W. Boyd from 1986 on the
smallest degree Newman polynomial that satises jf(z)j > 2 on
the unit circle @D. This polynomial is of degree 38 and we use this
special polynomial in our constructions. We also identify (without
a proof) all exceptional (k; n) with k 2 f1; 2; 3; n􀀀3; n􀀀2; n􀀀1g,
for which no such f0; 1g{polynomial of degree n exists: such pairs
are related to regular (real and complex) Pisot numbers.
Similar, but less complete results for f􀀀1; 1g polynomials are
established. We also look at the products of spaced Newman poly-
nomials and consider the rotated large Littlewood polynomials.
Lastly, based on our data, we formulate a natural conjecture about
the statistical distribution of N(f) in the set of Newman and Lit-
tlewood polynomials.