Identifier
Values
0 => 1 => 0
1 => 1 => 0
00 => 01 => 0
01 => 10 => 0
10 => 11 => 0
11 => 11 => 0
000 => 001 => 0
001 => 010 => 0
010 => 101 => 0
011 => 101 => 0
100 => 101 => 0
101 => 110 => 0
110 => 111 => 0
111 => 111 => 0
0000 => 0001 => 0
0001 => 0010 => 0
0010 => 0101 => 0
0011 => 0101 => 0
0100 => 1001 => 1
0101 => 1010 => 0
0110 => 1011 => 0
0111 => 1011 => 0
1000 => 1001 => 1
1001 => 1010 => 0
1010 => 1101 => 0
1011 => 1101 => 0
1100 => 1101 => 0
1101 => 1110 => 0
1110 => 1111 => 0
1111 => 1111 => 0
00000 => 00001 => 0
00001 => 00010 => 0
00010 => 00101 => 0
00011 => 00101 => 0
00100 => 01001 => 0
00101 => 01010 => 0
00110 => 01011 => 1
00111 => 01011 => 1
01000 => 10001 => 1
01001 => 10010 => 1
01010 => 10101 => 0
01011 => 10101 => 0
01100 => 10101 => 0
01101 => 10110 => 0
01110 => 10111 => 0
01111 => 10111 => 0
10000 => 10001 => 1
10001 => 10010 => 1
10010 => 10101 => 0
10011 => 10101 => 0
10100 => 11001 => 0
10101 => 11010 => 0
10110 => 11011 => 0
10111 => 11011 => 0
11000 => 11001 => 0
11001 => 11010 => 0
11010 => 11101 => 0
11011 => 11101 => 0
11100 => 11101 => 0
11101 => 11110 => 0
11110 => 11111 => 0
11111 => 11111 => 0
000000 => 000001 => 0
000001 => 000010 => 0
000010 => 000101 => 0
000011 => 000101 => 0
000100 => 001001 => 0
000101 => 001010 => 0
000110 => 001011 => 0
000111 => 001011 => 0
001000 => 010001 => 0
001001 => 010010 => 0
001010 => 010101 => 0
001011 => 010101 => 0
001100 => 010101 => 0
001101 => 010110 => 1
001110 => 010111 => 1
001111 => 010111 => 1
010000 => 100001 => 1
010001 => 100010 => 1
010010 => 100101 => 1
010011 => 100101 => 1
010100 => 101001 => 1
010101 => 101010 => 0
010110 => 101011 => 0
010111 => 101011 => 0
011000 => 101001 => 1
011001 => 101010 => 0
011010 => 101101 => 0
011011 => 101101 => 0
011100 => 101101 => 0
011101 => 101110 => 0
011110 => 101111 => 0
011111 => 101111 => 0
100000 => 100001 => 1
100001 => 100010 => 1
100010 => 100101 => 1
100011 => 100101 => 1
100100 => 101001 => 1
100101 => 101010 => 0
100110 => 101011 => 0
>>> Load all 1022 entries. <<<
100111 => 101011 => 0
101000 => 110001 => 1
101001 => 110010 => 0
101010 => 110101 => 0
101011 => 110101 => 0
101100 => 110101 => 0
101101 => 110110 => 0
101110 => 110111 => 0
101111 => 110111 => 0
110000 => 110001 => 1
110001 => 110010 => 0
110010 => 110101 => 0
110011 => 110101 => 0
110100 => 111001 => 0
110101 => 111010 => 0
110110 => 111011 => 0
110111 => 111011 => 0
111000 => 111001 => 0
111001 => 111010 => 0
111010 => 111101 => 0
111011 => 111101 => 0
111100 => 111101 => 0
111101 => 111110 => 0
111110 => 111111 => 0
111111 => 111111 => 0
0000000 => 0000001 => 0
0000001 => 0000010 => 0
0000010 => 0000101 => 0
0000011 => 0000101 => 0
0000100 => 0001001 => 0
0000101 => 0001010 => 0
0000110 => 0001011 => 0
0000111 => 0001011 => 0
0001000 => 0010001 => 0
0001001 => 0010010 => 0
0001010 => 0010101 => 0
0001011 => 0010101 => 0
0001100 => 0010101 => 0
0001101 => 0010110 => 0
0001110 => 0010111 => 1
0001111 => 0010111 => 1
0010000 => 0100001 => 0
0010001 => 0100010 => 0
0010010 => 0100101 => 0
0010011 => 0100101 => 0
0010100 => 0101001 => 0
0010101 => 0101010 => 0
0010110 => 0101011 => 1
0010111 => 0101011 => 1
0011000 => 0101001 => 0
0011001 => 0101010 => 0
0011010 => 0101101 => 1
0011011 => 0101101 => 1
0011100 => 0101101 => 1
0011101 => 0101110 => 1
0011110 => 0101111 => 1
0011111 => 0101111 => 1
0100000 => 1000001 => 1
0100001 => 1000010 => 1
0100010 => 1000101 => 1
0100011 => 1000101 => 1
0100100 => 1001001 => 1
0100101 => 1001010 => 1
0100110 => 1001011 => 2
0100111 => 1001011 => 2
0101000 => 1010001 => 1
0101001 => 1010010 => 1
0101010 => 1010101 => 0
0101011 => 1010101 => 0
0101100 => 1010101 => 0
0101101 => 1010110 => 0
0101110 => 1010111 => 0
0101111 => 1010111 => 0
0110000 => 1010001 => 1
0110001 => 1010010 => 1
0110010 => 1010101 => 0
0110011 => 1010101 => 0
0110100 => 1011001 => 0
0110101 => 1011010 => 0
0110110 => 1011011 => 0
0110111 => 1011011 => 0
0111000 => 1011001 => 0
0111001 => 1011010 => 0
0111010 => 1011101 => 0
0111011 => 1011101 => 0
0111100 => 1011101 => 0
0111101 => 1011110 => 0
0111110 => 1011111 => 0
0111111 => 1011111 => 0
1000000 => 1000001 => 1
1000001 => 1000010 => 1
1000010 => 1000101 => 1
1000011 => 1000101 => 1
1000100 => 1001001 => 1
1000101 => 1001010 => 1
1000110 => 1001011 => 2
1000111 => 1001011 => 2
1001000 => 1010001 => 1
1001001 => 1010010 => 1
1001010 => 1010101 => 0
1001011 => 1010101 => 0
1001100 => 1010101 => 0
1001101 => 1010110 => 0
1001110 => 1010111 => 0
1001111 => 1010111 => 0
1010000 => 1100001 => 1
1010001 => 1100010 => 1
1010010 => 1100101 => 0
1010011 => 1100101 => 0
1010100 => 1101001 => 0
1010101 => 1101010 => 0
1010110 => 1101011 => 0
1010111 => 1101011 => 0
1011000 => 1101001 => 0
1011001 => 1101010 => 0
1011010 => 1101101 => 0
1011011 => 1101101 => 0
1011100 => 1101101 => 0
1011101 => 1101110 => 0
1011110 => 1101111 => 0
1011111 => 1101111 => 0
1100000 => 1100001 => 1
1100001 => 1100010 => 1
1100010 => 1100101 => 0
1100011 => 1100101 => 0
1100100 => 1101001 => 0
1100101 => 1101010 => 0
1100110 => 1101011 => 0
1100111 => 1101011 => 0
1101000 => 1110001 => 0
1101001 => 1110010 => 0
1101010 => 1110101 => 0
1101011 => 1110101 => 0
1101100 => 1110101 => 0
1101101 => 1110110 => 0
1101110 => 1110111 => 0
1101111 => 1110111 => 0
1110000 => 1110001 => 0
1110001 => 1110010 => 0
1110010 => 1110101 => 0
1110011 => 1110101 => 0
1110100 => 1111001 => 0
1110101 => 1111010 => 0
1110110 => 1111011 => 0
1110111 => 1111011 => 0
1111000 => 1111001 => 0
1111001 => 1111010 => 0
1111010 => 1111101 => 0
1111011 => 1111101 => 0
1111100 => 1111101 => 0
1111101 => 1111110 => 0
1111110 => 1111111 => 0
1111111 => 1111111 => 0
00000000 => 00000001 => 0
00000001 => 00000010 => 0
00000010 => 00000101 => 0
00000011 => 00000101 => 0
00000100 => 00001001 => 0
00000101 => 00001010 => 0
00000110 => 00001011 => 0
00000111 => 00001011 => 0
00001000 => 00010001 => 0
00001001 => 00010010 => 0
00001010 => 00010101 => 0
00001011 => 00010101 => 0
00001100 => 00010101 => 0
00001101 => 00010110 => 0
00001110 => 00010111 => 0
00001111 => 00010111 => 0
00010000 => 00100001 => 0
00010001 => 00100010 => 0
00010010 => 00100101 => 0
00010011 => 00100101 => 0
00010100 => 00101001 => 0
00010101 => 00101010 => 0
00010110 => 00101011 => 0
00010111 => 00101011 => 0
00011000 => 00101001 => 0
00011001 => 00101010 => 0
00011010 => 00101101 => 0
00011011 => 00101101 => 0
00011100 => 00101101 => 0
00011101 => 00101110 => 1
00011110 => 00101111 => 1
00011111 => 00101111 => 1
00100000 => 01000001 => 0
00100001 => 01000010 => 0
00100010 => 01000101 => 0
00100011 => 01000101 => 0
00100100 => 01001001 => 0
00100101 => 01001010 => 0
00100110 => 01001011 => 0
00100111 => 01001011 => 0
00101000 => 01010001 => 0
00101001 => 01010010 => 0
00101010 => 01010101 => 0
00101011 => 01010101 => 0
00101100 => 01010101 => 0
00101101 => 01010110 => 1
00101110 => 01010111 => 1
00101111 => 01010111 => 1
00110000 => 01010001 => 0
00110001 => 01010010 => 0
00110010 => 01010101 => 0
00110011 => 01010101 => 0
00110100 => 01011001 => 2
00110101 => 01011010 => 1
00110110 => 01011011 => 1
00110111 => 01011011 => 1
00111000 => 01011001 => 2
00111001 => 01011010 => 1
00111010 => 01011101 => 1
00111011 => 01011101 => 1
00111100 => 01011101 => 1
00111101 => 01011110 => 1
00111110 => 01011111 => 1
00111111 => 01011111 => 1
01000000 => 10000001 => 1
01000001 => 10000010 => 1
01000010 => 10000101 => 1
01000011 => 10000101 => 1
01000100 => 10001001 => 1
01000101 => 10001010 => 1
01000110 => 10001011 => 1
01000111 => 10001011 => 1
01001000 => 10010001 => 1
01001001 => 10010010 => 1
01001010 => 10010101 => 1
01001011 => 10010101 => 1
01001100 => 10010101 => 1
01001101 => 10010110 => 2
01001110 => 10010111 => 2
01001111 => 10010111 => 2
01010000 => 10100001 => 1
01010001 => 10100010 => 1
01010010 => 10100101 => 1
01010011 => 10100101 => 1
01010100 => 10101001 => 1
01010101 => 10101010 => 0
01010110 => 10101011 => 0
01010111 => 10101011 => 0
01011000 => 10101001 => 1
01011001 => 10101010 => 0
01011010 => 10101101 => 0
01011011 => 10101101 => 0
01011100 => 10101101 => 0
01011101 => 10101110 => 0
01011110 => 10101111 => 0
01011111 => 10101111 => 0
01100000 => 10100001 => 1
01100001 => 10100010 => 1
01100010 => 10100101 => 1
01100011 => 10100101 => 1
01100100 => 10101001 => 1
01100101 => 10101010 => 0
01100110 => 10101011 => 0
01100111 => 10101011 => 0
01101000 => 10110001 => 1
01101001 => 10110010 => 0
01101010 => 10110101 => 0
01101011 => 10110101 => 0
01101100 => 10110101 => 0
01101101 => 10110110 => 0
01101110 => 10110111 => 0
01101111 => 10110111 => 0
01110000 => 10110001 => 1
01110001 => 10110010 => 0
01110010 => 10110101 => 0
01110011 => 10110101 => 0
01110100 => 10111001 => 0
01110101 => 10111010 => 0
01110110 => 10111011 => 0
01110111 => 10111011 => 0
01111000 => 10111001 => 0
01111001 => 10111010 => 0
01111010 => 10111101 => 0
01111011 => 10111101 => 0
01111100 => 10111101 => 0
01111101 => 10111110 => 0
01111110 => 10111111 => 0
01111111 => 10111111 => 0
10000000 => 10000001 => 1
10000001 => 10000010 => 1
10000010 => 10000101 => 1
10000011 => 10000101 => 1
10000100 => 10001001 => 1
10000101 => 10001010 => 1
10000110 => 10001011 => 1
10000111 => 10001011 => 1
10001000 => 10010001 => 1
10001001 => 10010010 => 1
10001010 => 10010101 => 1
10001011 => 10010101 => 1
10001100 => 10010101 => 1
10001101 => 10010110 => 2
10001110 => 10010111 => 2
10001111 => 10010111 => 2
10010000 => 10100001 => 1
10010001 => 10100010 => 1
10010010 => 10100101 => 1
10010011 => 10100101 => 1
10010100 => 10101001 => 1
10010101 => 10101010 => 0
10010110 => 10101011 => 0
10010111 => 10101011 => 0
10011000 => 10101001 => 1
10011001 => 10101010 => 0
10011010 => 10101101 => 0
10011011 => 10101101 => 0
10011100 => 10101101 => 0
10011101 => 10101110 => 0
10011110 => 10101111 => 0
10011111 => 10101111 => 0
10100000 => 11000001 => 1
10100001 => 11000010 => 1
10100010 => 11000101 => 1
10100011 => 11000101 => 1
10100100 => 11001001 => 1
10100101 => 11001010 => 0
10100110 => 11001011 => 0
10100111 => 11001011 => 0
10101000 => 11010001 => 1
10101001 => 11010010 => 0
10101010 => 11010101 => 0
10101011 => 11010101 => 0
10101100 => 11010101 => 0
10101101 => 11010110 => 0
10101110 => 11010111 => 0
10101111 => 11010111 => 0
10110000 => 11010001 => 1
10110001 => 11010010 => 0
10110010 => 11010101 => 0
10110011 => 11010101 => 0
10110100 => 11011001 => 0
10110101 => 11011010 => 0
10110110 => 11011011 => 0
10110111 => 11011011 => 0
10111000 => 11011001 => 0
10111001 => 11011010 => 0
10111010 => 11011101 => 0
10111011 => 11011101 => 0
10111100 => 11011101 => 0
10111101 => 11011110 => 0
10111110 => 11011111 => 0
10111111 => 11011111 => 0
11000000 => 11000001 => 1
11000001 => 11000010 => 1
11000010 => 11000101 => 1
11000011 => 11000101 => 1
11000100 => 11001001 => 1
11000101 => 11001010 => 0
11000110 => 11001011 => 0
11000111 => 11001011 => 0
11001000 => 11010001 => 1
11001001 => 11010010 => 0
11001010 => 11010101 => 0
11001011 => 11010101 => 0
11001100 => 11010101 => 0
11001101 => 11010110 => 0
11001110 => 11010111 => 0
11001111 => 11010111 => 0
11010000 => 11100001 => 1
11010001 => 11100010 => 0
11010010 => 11100101 => 0
11010011 => 11100101 => 0
11010100 => 11101001 => 0
11010101 => 11101010 => 0
11010110 => 11101011 => 0
11010111 => 11101011 => 0
11011000 => 11101001 => 0
11011001 => 11101010 => 0
11011010 => 11101101 => 0
11011011 => 11101101 => 0
11011100 => 11101101 => 0
11011101 => 11101110 => 0
11011110 => 11101111 => 0
11011111 => 11101111 => 0
11100000 => 11100001 => 1
11100001 => 11100010 => 0
11100010 => 11100101 => 0
11100011 => 11100101 => 0
11100100 => 11101001 => 0
11100101 => 11101010 => 0
11100110 => 11101011 => 0
11100111 => 11101011 => 0
11101000 => 11110001 => 0
11101001 => 11110010 => 0
11101010 => 11110101 => 0
11101011 => 11110101 => 0
11101100 => 11110101 => 0
11101101 => 11110110 => 0
11101110 => 11110111 => 0
11101111 => 11110111 => 0
11110000 => 11110001 => 0
11110001 => 11110010 => 0
11110010 => 11110101 => 0
11110011 => 11110101 => 0
11110100 => 11111001 => 0
11110101 => 11111010 => 0
11110110 => 11111011 => 0
11110111 => 11111011 => 0
11111000 => 11111001 => 0
11111001 => 11111010 => 0
11111010 => 11111101 => 0
11111011 => 11111101 => 0
11111100 => 11111101 => 0
11111101 => 11111110 => 0
11111110 => 11111111 => 0
11111111 => 11111111 => 0
000000000 => 000000001 => 0
000000001 => 000000010 => 0
000000010 => 000000101 => 0
000000011 => 000000101 => 0
000000100 => 000001001 => 0
000000101 => 000001010 => 0
000000110 => 000001011 => 0
000000111 => 000001011 => 0
000001000 => 000010001 => 0
000001001 => 000010010 => 0
000001010 => 000010101 => 0
000001011 => 000010101 => 0
000001100 => 000010101 => 0
000001101 => 000010110 => 0
000001110 => 000010111 => 0
000001111 => 000010111 => 0
000010000 => 000100001 => 0
000010001 => 000100010 => 0
000010010 => 000100101 => 0
000010011 => 000100101 => 0
000010100 => 000101001 => 0
000010101 => 000101010 => 0
000010110 => 000101011 => 0
000010111 => 000101011 => 0
000011000 => 000101001 => 0
000011001 => 000101010 => 0
000011010 => 000101101 => 0
000011011 => 000101101 => 0
000011100 => 000101101 => 0
000011101 => 000101110 => 0
000011110 => 000101111 => 1
000011111 => 000101111 => 1
000100000 => 001000001 => 0
000100001 => 001000010 => 0
000100010 => 001000101 => 0
000100011 => 001000101 => 0
000100100 => 001001001 => 0
000100101 => 001001010 => 0
000100110 => 001001011 => 0
000100111 => 001001011 => 0
000101000 => 001010001 => 0
000101001 => 001010010 => 0
000101010 => 001010101 => 0
000101011 => 001010101 => 0
000101100 => 001010101 => 0
000101101 => 001010110 => 0
000101110 => 001010111 => 1
000101111 => 001010111 => 1
000110000 => 001010001 => 0
000110001 => 001010010 => 0
000110010 => 001010101 => 0
000110011 => 001010101 => 0
000110100 => 001011001 => 0
000110101 => 001011010 => 0
000110110 => 001011011 => 1
000110111 => 001011011 => 1
000111000 => 001011001 => 0
000111001 => 001011010 => 0
000111010 => 001011101 => 1
000111011 => 001011101 => 1
000111100 => 001011101 => 1
000111101 => 001011110 => 1
000111110 => 001011111 => 1
000111111 => 001011111 => 1
001000000 => 010000001 => 0
001000001 => 010000010 => 0
001000010 => 010000101 => 0
001000011 => 010000101 => 0
001000100 => 010001001 => 0
001000101 => 010001010 => 0
001000110 => 010001011 => 0
001000111 => 010001011 => 0
001001000 => 010010001 => 0
001001001 => 010010010 => 0
001001010 => 010010101 => 0
001001011 => 010010101 => 0
001001100 => 010010101 => 0
001001101 => 010010110 => 0
001001110 => 010010111 => 1
001001111 => 010010111 => 1
001010000 => 010100001 => 0
001010001 => 010100010 => 0
001010010 => 010100101 => 0
001010011 => 010100101 => 0
001010100 => 010101001 => 0
001010101 => 010101010 => 0
001010110 => 010101011 => 1
001010111 => 010101011 => 1
001011000 => 010101001 => 0
001011001 => 010101010 => 0
001011010 => 010101101 => 1
001011011 => 010101101 => 1
001011100 => 010101101 => 1
001011101 => 010101110 => 1
001011110 => 010101111 => 1
001011111 => 010101111 => 1
001100000 => 010100001 => 0
001100001 => 010100010 => 0
001100010 => 010100101 => 0
001100011 => 010100101 => 0
001100100 => 010101001 => 0
001100101 => 010101010 => 0
001100110 => 010101011 => 1
001100111 => 010101011 => 1
001101000 => 010110001 => 2
001101001 => 010110010 => 2
001101010 => 010110101 => 1
001101011 => 010110101 => 1
001101100 => 010110101 => 1
001101101 => 010110110 => 1
001101110 => 010110111 => 1
001101111 => 010110111 => 1
001110000 => 010110001 => 2
001110001 => 010110010 => 2
001110010 => 010110101 => 1
001110011 => 010110101 => 1
001110100 => 010111001 => 1
001110101 => 010111010 => 1
001110110 => 010111011 => 1
001110111 => 010111011 => 1
001111000 => 010111001 => 1
001111001 => 010111010 => 1
001111010 => 010111101 => 1
001111011 => 010111101 => 1
001111100 => 010111101 => 1
001111101 => 010111110 => 1
001111110 => 010111111 => 1
001111111 => 010111111 => 1
010000000 => 100000001 => 1
010000001 => 100000010 => 1
010000010 => 100000101 => 1
010000011 => 100000101 => 1
010000100 => 100001001 => 1
010000101 => 100001010 => 1
010000110 => 100001011 => 1
010000111 => 100001011 => 1
010001000 => 100010001 => 1
010001001 => 100010010 => 1
010001010 => 100010101 => 1
010001011 => 100010101 => 1
010001100 => 100010101 => 1
010001101 => 100010110 => 1
010001110 => 100010111 => 2
010001111 => 100010111 => 2
010010000 => 100100001 => 1
010010001 => 100100010 => 1
010010010 => 100100101 => 1
010010011 => 100100101 => 1
010010100 => 100101001 => 1
010010101 => 100101010 => 1
010010110 => 100101011 => 2
010010111 => 100101011 => 2
010011000 => 100101001 => 1
010011001 => 100101010 => 1
010011010 => 100101101 => 2
010011011 => 100101101 => 2
010011100 => 100101101 => 2
010011101 => 100101110 => 2
010011110 => 100101111 => 2
010011111 => 100101111 => 2
010100000 => 101000001 => 1
010100001 => 101000010 => 1
010100010 => 101000101 => 1
010100011 => 101000101 => 1
010100100 => 101001001 => 1
010100101 => 101001010 => 1
010100110 => 101001011 => 2
010100111 => 101001011 => 2
010101000 => 101010001 => 1
010101001 => 101010010 => 1
010101010 => 101010101 => 0
010101011 => 101010101 => 0
010101100 => 101010101 => 0
010101101 => 101010110 => 0
010101110 => 101010111 => 0
010101111 => 101010111 => 0
010110000 => 101010001 => 1
010110001 => 101010010 => 1
010110010 => 101010101 => 0
010110011 => 101010101 => 0
010110100 => 101011001 => 0
010110101 => 101011010 => 0
010110110 => 101011011 => 0
010110111 => 101011011 => 0
010111000 => 101011001 => 0
010111001 => 101011010 => 0
010111010 => 101011101 => 0
010111011 => 101011101 => 0
010111100 => 101011101 => 0
010111101 => 101011110 => 0
010111110 => 101011111 => 0
010111111 => 101011111 => 0
011000000 => 101000001 => 1
011000001 => 101000010 => 1
011000010 => 101000101 => 1
011000011 => 101000101 => 1
011000100 => 101001001 => 1
011000101 => 101001010 => 1
011000110 => 101001011 => 2
011000111 => 101001011 => 2
011001000 => 101010001 => 1
011001001 => 101010010 => 1
011001010 => 101010101 => 0
011001011 => 101010101 => 0
011001100 => 101010101 => 0
011001101 => 101010110 => 0
011001110 => 101010111 => 0
011001111 => 101010111 => 0
011010000 => 101100001 => 1
011010001 => 101100010 => 1
011010010 => 101100101 => 0
011010011 => 101100101 => 0
011010100 => 101101001 => 0
011010101 => 101101010 => 0
011010110 => 101101011 => 0
011010111 => 101101011 => 0
011011000 => 101101001 => 0
011011001 => 101101010 => 0
011011010 => 101101101 => 0
011011011 => 101101101 => 0
011011100 => 101101101 => 0
011011101 => 101101110 => 0
011011110 => 101101111 => 0
011011111 => 101101111 => 0
011100000 => 101100001 => 1
011100001 => 101100010 => 1
011100010 => 101100101 => 0
011100011 => 101100101 => 0
011100100 => 101101001 => 0
011100101 => 101101010 => 0
011100110 => 101101011 => 0
011100111 => 101101011 => 0
011101000 => 101110001 => 0
011101001 => 101110010 => 0
011101010 => 101110101 => 0
011101011 => 101110101 => 0
011101100 => 101110101 => 0
011101101 => 101110110 => 0
011101110 => 101110111 => 0
011101111 => 101110111 => 0
011110000 => 101110001 => 0
011110001 => 101110010 => 0
011110010 => 101110101 => 0
011110011 => 101110101 => 0
011110100 => 101111001 => 0
011110101 => 101111010 => 0
011110110 => 101111011 => 0
011110111 => 101111011 => 0
011111000 => 101111001 => 0
011111001 => 101111010 => 0
011111010 => 101111101 => 0
011111011 => 101111101 => 0
011111100 => 101111101 => 0
011111101 => 101111110 => 0
011111110 => 101111111 => 0
011111111 => 101111111 => 0
100000000 => 100000001 => 1
100000001 => 100000010 => 1
100000010 => 100000101 => 1
100000011 => 100000101 => 1
100000100 => 100001001 => 1
100000101 => 100001010 => 1
100000110 => 100001011 => 1
100000111 => 100001011 => 1
100001000 => 100010001 => 1
100001001 => 100010010 => 1
100001010 => 100010101 => 1
100001011 => 100010101 => 1
100001100 => 100010101 => 1
100001101 => 100010110 => 1
100001110 => 100010111 => 2
100001111 => 100010111 => 2
100010000 => 100100001 => 1
100010001 => 100100010 => 1
100010010 => 100100101 => 1
100010011 => 100100101 => 1
100010100 => 100101001 => 1
100010101 => 100101010 => 1
100010110 => 100101011 => 2
100010111 => 100101011 => 2
100011000 => 100101001 => 1
100011001 => 100101010 => 1
100011010 => 100101101 => 2
100011011 => 100101101 => 2
100011100 => 100101101 => 2
100011101 => 100101110 => 2
100011110 => 100101111 => 2
100011111 => 100101111 => 2
100100000 => 101000001 => 1
100100001 => 101000010 => 1
100100010 => 101000101 => 1
100100011 => 101000101 => 1
100100100 => 101001001 => 1
100100101 => 101001010 => 1
100100110 => 101001011 => 2
100100111 => 101001011 => 2
100101000 => 101010001 => 1
100101001 => 101010010 => 1
100101010 => 101010101 => 0
100101011 => 101010101 => 0
100101100 => 101010101 => 0
100101101 => 101010110 => 0
100101110 => 101010111 => 0
100101111 => 101010111 => 0
100110000 => 101010001 => 1
100110001 => 101010010 => 1
100110010 => 101010101 => 0
100110011 => 101010101 => 0
100110100 => 101011001 => 0
100110101 => 101011010 => 0
100110110 => 101011011 => 0
100110111 => 101011011 => 0
100111000 => 101011001 => 0
100111001 => 101011010 => 0
100111010 => 101011101 => 0
100111011 => 101011101 => 0
100111100 => 101011101 => 0
100111101 => 101011110 => 0
100111110 => 101011111 => 0
100111111 => 101011111 => 0
101000000 => 110000001 => 1
101000001 => 110000010 => 1
101000010 => 110000101 => 1
101000011 => 110000101 => 1
101000100 => 110001001 => 1
101000101 => 110001010 => 1
101000110 => 110001011 => 2
101000111 => 110001011 => 2
101001000 => 110010001 => 1
101001001 => 110010010 => 1
101001010 => 110010101 => 0
101001011 => 110010101 => 0
101001100 => 110010101 => 0
101001101 => 110010110 => 0
101001110 => 110010111 => 0
101001111 => 110010111 => 0
101010000 => 110100001 => 1
101010001 => 110100010 => 1
101010010 => 110100101 => 0
101010011 => 110100101 => 0
101010100 => 110101001 => 0
101010101 => 110101010 => 0
101010110 => 110101011 => 0
101010111 => 110101011 => 0
101011000 => 110101001 => 0
101011001 => 110101010 => 0
101011010 => 110101101 => 0
101011011 => 110101101 => 0
101011100 => 110101101 => 0
101011101 => 110101110 => 0
101011110 => 110101111 => 0
101011111 => 110101111 => 0
101100000 => 110100001 => 1
101100001 => 110100010 => 1
101100010 => 110100101 => 0
101100011 => 110100101 => 0
101100100 => 110101001 => 0
101100101 => 110101010 => 0
101100110 => 110101011 => 0
101100111 => 110101011 => 0
101101000 => 110110001 => 0
101101001 => 110110010 => 0
101101010 => 110110101 => 0
101101011 => 110110101 => 0
101101100 => 110110101 => 0
101101101 => 110110110 => 0
101101110 => 110110111 => 0
101101111 => 110110111 => 0
101110000 => 110110001 => 0
101110001 => 110110010 => 0
101110010 => 110110101 => 0
101110011 => 110110101 => 0
101110100 => 110111001 => 0
101110101 => 110111010 => 0
101110110 => 110111011 => 0
101110111 => 110111011 => 0
101111000 => 110111001 => 0
101111001 => 110111010 => 0
101111010 => 110111101 => 0
101111011 => 110111101 => 0
101111100 => 110111101 => 0
101111101 => 110111110 => 0
101111110 => 110111111 => 0
101111111 => 110111111 => 0
110000000 => 110000001 => 1
110000001 => 110000010 => 1
110000010 => 110000101 => 1
110000011 => 110000101 => 1
110000100 => 110001001 => 1
110000101 => 110001010 => 1
110000110 => 110001011 => 2
110000111 => 110001011 => 2
110001000 => 110010001 => 1
110001001 => 110010010 => 1
110001010 => 110010101 => 0
110001011 => 110010101 => 0
110001100 => 110010101 => 0
110001101 => 110010110 => 0
110001110 => 110010111 => 0
110001111 => 110010111 => 0
110010000 => 110100001 => 1
110010001 => 110100010 => 1
110010010 => 110100101 => 0
110010011 => 110100101 => 0
110010100 => 110101001 => 0
110010101 => 110101010 => 0
110010110 => 110101011 => 0
110010111 => 110101011 => 0
110011000 => 110101001 => 0
110011001 => 110101010 => 0
110011010 => 110101101 => 0
110011011 => 110101101 => 0
110011100 => 110101101 => 0
110011101 => 110101110 => 0
110011110 => 110101111 => 0
110011111 => 110101111 => 0
110100000 => 111000001 => 1
110100001 => 111000010 => 1
110100010 => 111000101 => 0
110100011 => 111000101 => 0
110100100 => 111001001 => 0
110100101 => 111001010 => 0
110100110 => 111001011 => 0
110100111 => 111001011 => 0
110101000 => 111010001 => 0
110101001 => 111010010 => 0
110101010 => 111010101 => 0
110101011 => 111010101 => 0
110101100 => 111010101 => 0
110101101 => 111010110 => 0
110101110 => 111010111 => 0
110101111 => 111010111 => 0
110110000 => 111010001 => 0
110110001 => 111010010 => 0
110110010 => 111010101 => 0
110110011 => 111010101 => 0
110110100 => 111011001 => 0
110110101 => 111011010 => 0
110110110 => 111011011 => 0
110110111 => 111011011 => 0
110111000 => 111011001 => 0
110111001 => 111011010 => 0
110111010 => 111011101 => 0
110111011 => 111011101 => 0
110111100 => 111011101 => 0
110111101 => 111011110 => 0
110111110 => 111011111 => 0
110111111 => 111011111 => 0
111000000 => 111000001 => 1
111000001 => 111000010 => 1
111000010 => 111000101 => 0
111000011 => 111000101 => 0
111000100 => 111001001 => 0
111000101 => 111001010 => 0
111000110 => 111001011 => 0
111000111 => 111001011 => 0
111001000 => 111010001 => 0
111001001 => 111010010 => 0
111001010 => 111010101 => 0
111001011 => 111010101 => 0
111001100 => 111010101 => 0
111001101 => 111010110 => 0
111001110 => 111010111 => 0
111001111 => 111010111 => 0
111010000 => 111100001 => 0
111010001 => 111100010 => 0
111010010 => 111100101 => 0
111010011 => 111100101 => 0
111010100 => 111101001 => 0
111010101 => 111101010 => 0
111010110 => 111101011 => 0
111010111 => 111101011 => 0
111011000 => 111101001 => 0
111011001 => 111101010 => 0
111011010 => 111101101 => 0
111011011 => 111101101 => 0
111011100 => 111101101 => 0
111011101 => 111101110 => 0
111011110 => 111101111 => 0
111011111 => 111101111 => 0
111100000 => 111100001 => 0
111100001 => 111100010 => 0
111100010 => 111100101 => 0
111100011 => 111100101 => 0
111100100 => 111101001 => 0
111100101 => 111101010 => 0
111100110 => 111101011 => 0
111100111 => 111101011 => 0
111101000 => 111110001 => 0
111101001 => 111110010 => 0
111101010 => 111110101 => 0
111101011 => 111110101 => 0
111101100 => 111110101 => 0
111101101 => 111110110 => 0
111101110 => 111110111 => 0
111101111 => 111110111 => 0
111110000 => 111110001 => 0
111110001 => 111110010 => 0
111110010 => 111110101 => 0
111110011 => 111110101 => 0
111110100 => 111111001 => 0
111110101 => 111111010 => 0
111110110 => 111111011 => 0
111110111 => 111111011 => 0
111111000 => 111111001 => 0
111111001 => 111111010 => 0
111111010 => 111111101 => 0
111111011 => 111111101 => 0
111111100 => 111111101 => 0
111111101 => 111111110 => 0
111111110 => 111111111 => 0
111111111 => 111111111 => 0
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Description
The number of times the path corresponding to a binary word crosses the base line.
Interpret each $0$ as a step $(1,-1)$ and $1$ as a step $(1,1)$. Then this statistic counts the number of times the path crosses the $x$-axis.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.