Copyright © 2024 Kees Krijnen
Audio companding 16-bit two's complement
13-bits significant (including sign) 20-bits value companding to 16-bits value 13 bits ~ 78 dB psychoacoustic masking -> 20 bits ~ 120 dB dynamic range 0 1 abcdefghijkl 000000 -> 0 111 abcdefghijkl 0 01 abcdefghijkl 00000 -> 0 110 abcdefghijkl 0 001 abcdefghijkl 0000 -> 0 101 abcdefghijkl 0 0001 abcdefghijkl 000 -> 0 100 abcdefghijkl 0 00001 abcdefghijkl 00 -> 0 011 abcdefghijkl 0 000001 abcdefghijkl 0 -> 0 010 abcdefghijkl 0 0000001 abcdefghijkl -> 0 001 abcdefghijkl 0 0000000 abcdefghijkl -> 0 000 abcdefghijkl 1 0 abcdefghijkl 111111 -> 1 000 abcdefghijkl 1 10 abcdefghijkl 11111 -> 1 001 abcdefghijkl 1 110 abcdefghijkl 1111 -> 1 010 abcdefghijkl 1 1110 abcdefghijkl 111 -> 1 011 abcdefghijkl 1 11110 abcdefghijkl 11 -> 1 100 abcdefghijkl 1 111110 abcdefghijkl 1 -> 1 101 abcdefghijkl 1 1111110 abcdefghijkl -> 1 110 abcdefghijkl 1 1111111 abcdefghijkl -> 1 111 abcdefghijkl 2-bits significant (including sign) 9-bits value companding to 5-bits value 0 1 a 000000 -> 0 111 a 0 1 0 000000 -> 0 111 0 128 -> 14 0 1 1 000000 -> 0 111 1 192 -> 15 0 01 a 00000 -> 0 110 a 0 01 0 00000 -> 0 110 0 64 -> 12 0 01 1 00000 -> 0 110 1 96 -> 13 0 001 a 0000 -> 0 101 a 0 001 0 0000 -> 0 101 0 32 -> 10 0 001 1 0000 -> 0 101 1 48 -> 11 0 0001 a 000 -> 0 100 a 0 0001 0 000 -> 0 100 0 16 -> 8 0 0001 1 000 -> 0 100 1 24 -> 9 0 00001 a 00 -> 0 011 a 0 00001 0 00 -> 0 011 0 8 -> 6 0 00001 1 00 -> 0 011 1 12 -> 7 0 000001 a 0 -> 0 010 a 0 000001 0 0 -> 0 010 0 4 -> 4 0 000001 1 0 -> 0 010 1 6 -> 5 0 0000001 a -> 0 001 a 0 0000001 0 -> 0 001 0 2 -> 2 0 0000001 1 -> 0 001 1 3 -> 3 0 0000000 a -> 0 000 a 0 0000000 0 -> 0 000 0 0 -> 0 0 0000000 1 -> 0 000 1 1 -> 1 1 0 a 111111 -> 1 000 a 1 0 0 111111 -> 1 000 0 -193 -> -16 1 0 1 111111 -> 1 000 1 -129 -> -15 1 10 a 11111 -> 1 001 a 1 10 0 11111 -> 1 001 0 -97 -> -14 1 10 1 11111 -> 1 001 1 -65 -> -13 1 110 a 1111 -> 1 010 a 1 110 0 1111 -> 1 010 0 -53 -> -12 1 110 1 1111 -> 1 010 1 -33 -> -11 1 1110 a 111 -> 1 011 a 1 1110 0 111 -> 1 011 0 -25 -> -10 1 1110 1 111 -> 1 011 1 -17 -> -9 1 11110 a 11 -> 1 100 a 1 11110 0 11 -> 1 100 0 -13 -> -8 1 11110 1 11 -> 1 100 1 -9 -> -7 1 111110 a 1 -> 1 101 a 1 111110 0 1 -> 1 101 0 -7 -> -6 1 111110 1 1 -> 1 101 1 -5 -> -5 1 1111110 a -> 1 110 a 1 1111110 0 -> 1 110 0 -4 -> -4 1 1111110 1 -> 1 110 1 -3 -> -3 1 1111111 a -> 1 111 a 1 1111111 0 -> 1 111 0 -2 -> -2 1 1111111 1 -> 1 111 1 -1 -> -1 12-bits significant (including sign) 28-bits value companding to 16-bits value 12 bits ~ 72 dB psychoacoustic masking -> 28 bits ~ 168 dB dynamic range 0 1 abcdefghijk 000000000000000 -> 0 1111 abcdefghijk 0 01 abcdefghijk 00000000000000 -> 0 1110 abcdefghijk 0 001 abcdefghijk 0000000000000 -> 0 1011 abcdefghijk 0 0001 abcdefghijk 000000000000 -> 0 1100 abcdefghijk 0 00001 abcdefghijk 00000000000 -> 0 1011 abcdefghijk 0 000001 abcdefghijk 0000000000 -> 0 1010 abcdefghijk 0 0000001 abcdefghijk 000000000 -> 0 1001 abcdefghijk 0 00000001 abcdefghijk 00000000 -> 0 1000 abcdefghijk 0 000000001 abcdefghijkl 000000 -> 0 0111 abcdefghijk 0 0000000001 abcdefghijkl 00000 -> 0 0110 abcdefghijk 0 00000000001 abcdefghijkl 0000 -> 0 0011 abcdefghijk 0 000000000001 abcdefghijkl 000 -> 0 0100 abcdefghijk 0 0000000000001 abcdefghijkl 00 -> 0 0011 abcdefghijk 0 00000000000001 abcdefghijkl 0 -> 0 0010 abcdefghijk 0 000000000000001 abcdefghijkl -> 0 0001 abcdefghijk 0 000000000000000 abcdefghijkl -> 0 0000 abcdefghijk 1 0 abcdefghijkl 11111111111111 -> 1 0000 abcdefghijk 1 10 abcdefghijkl 1111111111111 -> 1 0001 abcdefghijk 1 110 abcdefghijkl 111111111111 -> 1 0010 abcdefghijk 1 1110 abcdefghijkl 11111111111 -> 1 0011 abcdefghijk 1 11110 abcdefghijkl 1111111111 -> 1 0100 abcdefghijk 1 111110 abcdefghijkl 111111111 -> 1 0101 abcdefghijk 1 1111110 abcdefghijkl 11111111 -> 1 0110 abcdefghijk 1 11111110 abcdefghijkl 1111111 -> 1 0111 abcdefghijk 1 111111110 abcdefghijkl 111111 -> 1 1000 abcdefghijk 1 1111111110 abcdefghijkl 11111 -> 1 1001 abcdefghijk 1 11111111110 abcdefghijkl 1111 -> 1 1010 abcdefghijk 1 111111111110 abcdefghijkl 111 -> 1 1011 abcdefghijk 1 1111111111110 abcdefghijkl 11 -> 1 1100 abcdefghijk 1 11111111111110 abcdefghijkl 1 -> 1 1101 abcdefghijk 1 111111111111110 abcdefghijkl -> 1 1110 abcdefghijk 1 111111111111111 abcdefghijkl -> 1 1111 abcdefghijk 2-bits significant (including sign) 17-bits value companding to 6-bits value 0 1 a 00000000000000 -> 0 1111 a 0 1 0 00000000000000 -> 0 1111 0 32768 -> 30 0 1 1 00000000000000 -> 0 1111 1 49152 -> 31 0 01 a 0000000000000 -> 0 1110 a 0 01 0 0000000000000 -> 0 1110 0 16384 -> 28 0 01 1 0000000000000 -> 0 1110 1 24578 -> 29 0 001 a 000000000000 -> 0 1101 a 0 001 0 000000000000 -> 0 1101 0 8192 -> 26 0 001 1 000000000000 -> 0 1101 1 12288 -> 27 0 0001 a 00000000000 -> 0 1100 a 0 0001 0 00000000000 -> 0 1100 0 4096 -> 24 0 0001 1 00000000000 -> 0 1100 1 6144 -> 25 0 00001 a 0000000000 -> 0 1011 a 0 00001 0 0000000000 -> 0 1011 0 2048 -> 22 0 00001 1 0000000000 -> 0 1011 1 3072 -> 23 0 000001 a 000000000 -> 0 1010 a 0 000001 0 000000000 -> 0 1010 0 1024 -> 20 0 000001 1 000000000 -> 0 1010 1 1536 -> 21 0 0000001 a 00000000 -> 0 1001 a 0 0000001 0 00000000 -> 0 1001 0 512 -> 18 0 0000001 1 00000000 -> 0 1001 1 768 -> 19 0 00000001 a 0000000 -> 0 1000 a 0 00000001 0 0000000 -> 0 1000 0 256 -> 16 0 00000001 1 0000000 -> 0 1000 1 384 -> 17 0 000000001 a 000000 -> 0 0111 a 0 000000001 0 000000 -> 0 0111 0 128 -> 14 0 000000001 1 000000 -> 0 0111 1 192 -> 15 0 0000000001 a 00000 -> 0 0110 a 0 0000000001 0 00000 -> 0 0110 0 64 -> 12 0 0000000001 1 00000 -> 0 0110 1 96 -> 13 0 00000000001 a 0000 -> 0 0101 a 0 00000000001 0 0000 -> 0 0101 0 32 -> 10 0 00000000001 1 0000 -> 0 0101 1 48 -> 11 0 000000000001 a 000 -> 0 0100 a 0 000000000001 0 000 -> 0 0100 0 16 -> 8 0 000000000001 1 000 -> 0 0100 1 24 -> 9 0 0000000000001 a 00 -> 0 0011 a 0 0000000000001 0 00 -> 0 0011 0 8 -> 6 0 0000000000001 1 00 -> 0 0011 1 12 -> 7 0 00000000000001 a 0 -> 0 0010 a 0 00000000000001 0 0 -> 0 0010 0 4 -> 4 0 00000000000001 1 0 -> 0 0010 1 6 -> 5 0 000000000000001 a -> 0 0001 a 0 000000000000001 0 -> 0 0001 0 2 -> 2 0 000000000000001 1 -> 0 0001 1 3 -> 3 0 000000000000000 a -> 0 0000 a 0 000000000000000 0 -> 0 0000 0 0 -> 0 0 000000000000000 1 -> 0 0000 1 1 -> 1 1 0 a 11111111111111 -> 1 0000 a 1 0 0 11111111111111 -> 1 0000 0 -49153 -> -32 1 0 1 11111111111111 -> 1 0000 1 -32769 -> -31 1 10 a 1111111111111 -> 1 0001 a 1 10 0 1111111111111 -> 1 0001 0 -24577 -> -30 1 10 1 1111111111111 -> 1 0001 1 -16385 -> -29 1 110 a 111111111111 -> 1 0010 a 1 110 0 111111111111 -> 1 0010 0 -12289 -> -28 1 110 1 111111111111 -> 1 0010 1 -8193 -> -27 1 1110 a 11111111111 -> 1 0011 a 1 1110 0 11111111111 -> 1 0011 0 -6145 -> -26 1 1110 1 11111111111 -> 1 0011 1 -4097 -> -25 1 11110 a 1111111111 -> 1 0100 a 1 11110 0 1111111111 -> 1 0100 0 -3073 -> -24 1 11110 1 1111111111 -> 1 0100 1 -2049 -> -23 1 111110 a 111111111 -> 1 0101 a 1 111110 0 111111111 -> 1 0101 0 -1537 -> -22 1 111110 1 111111111 -> 1 0101 1 -1025 -> -21 1 1111110 a 11111111 -> 1 0110 a 1 1111110 0 11111111 -> 1 0110 0 -769 -> -20 1 1111110 1 11111111 -> 1 0110 1 -513 -> -19 1 11111110 a 1111111 -> 1 0111 a 1 11111110 0 1111111 -> 1 0111 0 -385 -> -18 1 11111110 1 1111111 -> 1 0111 1 -257 -> -17 1 111111110 a 111111 -> 1 1000 a 1 111111110 0 111111 -> 1 1000 0 -193 -> -16 1 111111110 1 111111 -> 1 1000 1 -129 -> -15 1 1111111110 a 11111 -> 1 1001 a 1 1111111110 0 11111 -> 1 1001 0 -97 -> -14 1 1111111110 1 11111 -> 1 1001 1 -65 -> -13 1 11111111110 a 1111 -> 1 1010 a 1 11111111110 0 1111 -> 1 1010 0 -53 -> -12 1 11111111110 1 1111 -> 1 1010 1 -33 -> -11 1 111111111110 a 111 -> 1 1011 a 1 111111111110 0 111 -> 1 1011 0 -25 -> -10 1 111111111110 1 111 -> 1 1011 1 -17 -> -9 1 1111111111110 a 11 -> 1 1100 a 1 1111111111110 0 11 -> 1 1100 0 -13 -> -8 1 1111111111110 1 11 -> 1 1100 1 -9 -> -7 1 11111111111110 a 1 -> 1 1101 a 1 11111111111110 0 1 -> 1 1101 0 -7 -> -6 1 11111111111110 1 1 -> 1 1101 1 -5 -> -5 1 111111111111110 a -> 1 1110 a 1 111111111111110 0 -> 1 1110 0 -4 -> -4 1 111111111111110 1 -> 1 1110 1 -3 -> -3 1 111111111111111 a -> 1 1111 a 1 111111111111111 0 -> 1 1111 0 -2 -> -2 1 111111111111111 1 -> 1 1111 1 -1 -> -1