The NACA four digit wing sections were derived to have the same thickness distribution as the Göttingen 398 and the Clark Y airfoils when their camber was removed. These airfoils were noted as being particularly efficient by the designers of the NACA family.
The 4-digit thickness distribution is given by the following equation:
y = (t/c) * ( A sqrt(x) + B x + C x2 + D x3 + E x4 )
where ** denotes exponentiation, (t/c) is the maximum thickness to chord ratio of the airfoil, x is the position as fraction of chord, and y is the half-thickness as fraction of chord.
The coefficients are:
A = 1.4845
B = -0.630
C = -1.758
D = 1.4215
E = -0.5075
You may note that these numbers are 5 times the values usually shown in references. The usual numbers are for computing a 20 percent airfoil which you are then expected to scale to your desired thickness.
Of course, for computing efficiency, y is computed from
y=(t/c)*(A sqrt(x) + x*(B + x*(C + x*(D + x*E)))))
Be sure to note that y is the HALF-THICKNESS. The maximum thickness ocurrs at approximately 30 percent of chord.
Also note that the trailing edge thickness is NOT zero.