# binary memoryless source, P(0) = p; redundancy in bits per source # symbol of a Huffman code over blocks of k symbols p H k=1 k=2 k=4 k=8 0.500 1.00000 0.00000 0.00000 0.00000 0.00000 0.505 0.99993 0.00007 0.00007 0.00007 0.00007 0.510 0.99971 0.00029 0.00029 0.00029 0.00029 0.515 0.99935 0.00065 0.00065 0.00065 0.00065 0.520 0.99885 0.00115 0.00115 0.00115 0.00115 0.525 0.99820 0.00180 0.00180 0.00180 0.00176 0.530 0.99740 0.00260 0.00260 0.00260 0.00240 0.535 0.99646 0.00354 0.00354 0.00354 0.00291 0.540 0.99538 0.00462 0.00462 0.00462 0.00327 0.545 0.99415 0.00585 0.00585 0.00585 0.00360 0.550 0.99277 0.00723 0.00723 0.00713 0.00376 0.555 0.99125 0.00875 0.00875 0.00706 0.00402 0.560 0.98959 0.01041 0.01041 0.00712 0.00403 0.565 0.98777 0.01223 0.01223 0.00733 0.00378 0.570 0.98582 0.01418 0.01418 0.00767 0.00363 0.575 0.98371 0.01629 0.01629 0.00815 0.00351 0.580 0.98145 0.01855 0.01855 0.00878 0.00353 0.585 0.97905 0.02095 0.02095 0.00954 0.00368 0.590 0.97650 0.02350 0.02350 0.00972 0.00358 0.595 0.97380 0.02620 0.02620 0.00991 0.00346 0.600 0.97095 0.02905 0.02905 0.01025 0.00349 0.605 0.96795 0.03205 0.03205 0.01074 0.00343 0.610 0.96480 0.03520 0.03520 0.01138 0.00329 0.615 0.96150 0.03850 0.03850 0.01217 0.00328 0.620 0.95804 0.04196 0.03976 0.01269 0.00339 0.625 0.95443 0.04557 0.03775 0.01273 0.00358 0.630 0.95067 0.04933 0.03588 0.01295 0.00370 0.635 0.94676 0.05324 0.03413 0.01334 0.00397 0.640 0.94268 0.05732 0.03252 0.01391 0.00438 0.645 0.93845 0.06155 0.03103 0.01466 0.00493 0.650 0.93407 0.06593 0.02968 0.01559 0.00562 0.655 0.92952 0.07048 0.02846 0.01669 0.00646 0.660 0.92482 0.07518 0.02738 0.01798 0.00744 0.665 0.91995 0.08005 0.02643 0.01945 0.00856 0.670 0.91493 0.08507 0.02562 0.01905 0.00827 0.675 0.90974 0.09026 0.02495 0.01779 0.00731 0.680 0.90438 0.09562 0.02442 0.01667 0.00650 0.685 0.89886 0.10114 0.02403 0.01520 0.00582 0.690 0.89317 0.10683 0.02378 0.01346 0.00528 0.695 0.88732 0.11268 0.02367 0.01189 0.00488 0.700 0.88129 0.11871 0.02371 0.01051 0.00457 0.705 0.87509 0.12491 0.02389 0.00930 0.00438 0.710 0.86872 0.13128 0.02423 0.00828 0.00433 0.715 0.86217 0.13783 0.02471 0.00745 0.00434 0.720 0.85545 0.14455 0.02535 0.00681 0.00427 0.725 0.84855 0.15145 0.02614 0.00635 0.00432 0.730 0.84146 0.15854 0.02709 0.00610 0.00456 0.735 0.83420 0.16580 0.02819 0.00604 0.00497 0.740 0.82675 0.17325 0.02945 0.00618 0.00525 0.745 0.81911 0.18089 0.03088 0.00653 0.00478 0.750 0.81128 0.18872 0.03247 0.00708 0.00448 0.755 0.80326 0.19674 0.03423 0.00785 0.00436 0.760 0.79504 0.20496 0.03616 0.00883 0.00436 0.765 0.78663 0.21337 0.03826 0.01003 0.00441 0.770 0.77801 0.22199 0.04054 0.01145 0.00465 0.775 0.76919 0.23081 0.04299 0.01309 0.00510 0.780 0.76017 0.23983 0.04563 0.01497 0.00575 0.785 0.75093 0.24907 0.04846 0.01708 0.00661 0.790 0.74148 0.25852 0.05147 0.01943 0.00762 0.795 0.73182 0.26818 0.05467 0.01999 0.00886 0.800 0.72193 0.27807 0.05807 0.01887 0.01030 0.805 0.71181 0.28819 0.06167 0.01714 0.00900 0.810 0.70147 0.29853 0.06548 0.01557 0.00789 0.815 0.69089 0.30911 0.06949 0.01405 0.00698 0.820 0.68008 0.31992 0.07372 0.01276 0.00627 0.825 0.66902 0.33098 0.07817 0.01170 0.00572 0.830 0.65770 0.34230 0.08285 0.01088 0.00536 0.835 0.64614 0.35386 0.08775 0.01031 0.00510 0.840 0.63431 0.36569 0.09289 0.00999 0.00470 0.845 0.62221 0.37779 0.09827 0.00992 0.00458 0.850 0.60984 0.39016 0.10391 0.01013 0.00470 0.855 0.59719 0.40281 0.10980 0.01060 0.00466 0.860 0.58424 0.41576 0.11596 0.01136 0.00469 0.865 0.57099 0.42901 0.12239 0.01240 0.00478 0.870 0.55744 0.44256 0.12911 0.01351 0.00519 0.875 0.54356 0.45644 0.13612 0.01417 0.00595 0.880 0.52936 0.47064 0.14344 0.01522 0.00711 0.885 0.51482 0.48518 0.15107 0.01667 0.00868 0.890 0.49992 0.50008 0.15903 0.01853 0.00979 0.895 0.48465 0.51535 0.16734 0.02082 0.00813 0.900 0.46900 0.53100 0.17600 0.02355 0.00680 0.905 0.45294 0.54706 0.18504 0.02675 0.00579 0.910 0.43647 0.56353 0.19448 0.03044 0.00515 0.915 0.41956 0.58044 0.20433 0.03463 0.00442 0.920 0.40218 0.59782 0.21462 0.03936 0.00408 0.925 0.38431 0.61569 0.22538 0.04465 0.00425 0.930 0.36592 0.63408 0.23663 0.05053 0.00496 0.935 0.34698 0.65302 0.24841 0.05704 0.00624 0.940 0.32744 0.67256 0.26076 0.06422 0.00814 0.945 0.30727 0.69273 0.27372 0.07212 0.00992 0.950 0.28640 0.71360 0.28735 0.08079 0.01238 0.955 0.26477 0.73523 0.30172 0.09031 0.01575 0.960 0.24229 0.75771 0.31691 0.10075 0.02014 0.965 0.21888 0.78112 0.33301 0.11222 0.02565 0.970 0.19439 0.80561 0.35016 0.12484 0.03216 0.975 0.16866 0.83134 0.36853 0.13880 0.03995 0.980 0.14144 0.85856 0.38836 0.15434 0.04962 0.985 0.11236 0.88764 0.41003 0.17183 0.06154 0.990 0.08079 0.91921 0.43416 0.19190 0.07637 0.999 0.01141 0.98859 0.49009 0.24084 0.11673