1. A method for producing a digital halftone monochrome output bitmap comprising the steps of: (a) obtaining an input bitmap of identical dimensions to said output bitmap in pixels high and wide, within which each pixel's analog gray level is expressed as a multi-bit value; (b) subdividing said input bitmap into a plurality of multi-pixel supercells of identical dimensions in pixels high and wide; (c) subdividing said supercells into two-pixel-by-two-pixel subcells and determining an analog gray level expressed as a multi-bit value for each of said subcells; (d) dividing each said subcell gray level by one whole monochrome output pixel expressed as a multi-bit value to yield I, a two-pixel-by-two-pixel subcell monochrome interim level in whole output pixels, and R, a two-pixel-by-two-pixel subcell remainder, a partial pixel gray level expressed as a multi-bit value, for each said subcell; (e) combining said subcells into a plurality of larger subcells of identical dimensions in pixels high and wide so that all said larger subcells are contained within said supercell; (f) determining larger subcell analog input gray levels expressed as a multi-bit value for each of said larger subcells; (g) dividing each said larger subcell gray level by one while monochrome output pixel expressed as a multi-bit value to yield I, a larger subcell monochrome interim level in whole output pixels, and R, a larger subcell remainder, a partial pixel gray level expressed as a multi-bit value, for each said larger subcell; (h) combining said larger subcells into said supercell and determining an analog supercell input gray level expressed as a multi-bit value; (i) determining for said supercell a monochrome output final gray level F by dividing its input gray level by one whole monochrome output pixel expressed as a multi-bit value and rounding up or down to the nearest whole pixel; (j) obtaining a sum of said monochrome interim levels I of said supercell's next smaller contained larger subcells and comparing said sum to said supercell's monochrome output final gray level F; (k) utilizing a derived shortfall, if any, to determine said larger subcells' individual monochrome output final gray levels F by allocating one whole monochrome output pixel to each of said larger subcells according to a sorting of said larger subcells' remainders R until parity with said supercell is achieved; (l) obtaining a sum of the monochrome interim levels I of each of said larger subcell's contained two-pixel-by-two-pixel subcells and comparing said sum to said larger subcell's monochrome output final gray level F; (m) utilizing a derived shortfall, if any, to determine said two-pixel-by-two-pixel subcells' individual monochrome output final gray levels F by allocating one whole monochrome output pixel to each of said two-pixel-by-two-pixel subcells according to a sorting of said two-pixel-by-two-pixel subcells' remainders R until parity with said larger subcell is achieved; (n) setting the final monochrome output patterns for each of said two-pixel-by-two-pixel subcells; and (o) recombining all of said two-pixel-by-two-pixel monochrome output subcells into said digital halftone monochrome output bitmap.