How many combinations are possible with 5 bits?

;WITH x AS ( SELECT x FROM (VALUES('0'),('1')) AS y(x) ) SELECT A = x.x, B = x2.x, C = x3.x, D = x4.x, E = x5.x, [binary] = x.x + x2.x + x3.x + x4.x + x5.x FROM x CROSS JOIN x AS x2 CROSS JOIN x AS x3 CROSS JOIN x AS x4 CROSS JOIN x AS x5; Or, more lazily and less explicitly:

;WITH x AS ( SELECT x FROM (VALUES('0'),('1')) AS y(x) ) SELECT A = x.x, B = x2.x, C = x3.x, D = x4.x, E = x5.x, [binary] = x.x + x2.x + x3.x + x4.x + x5.x FROM x, x AS x2, x AS x3, x AS x4, x AS x5; Results:

A B C D E binary


0 0 0 0 0 00000 0 1 0 0 0 01000 0 0 1 0 0 00100 0 1 1 0 0 01100 0 0 0 1 0 00010 0 1 0 1 0 01010 0 0 1 1 0 00110 0 1 1 1 0 01110 1 0 0 0 0 10000 1 1 0 0 0 11000 1 0 1 0 0 10100 1 1 1 0 0 11100 1 0 0 1 0 10010 1 1 0 1 0 11010 1 0 1 1 0 10110 1 1 1 1 0 11110 0 0 0 0 1 00001 0 1 0 0 1 01001 0 0 1 0 1 00101 0 1 1 0 1 01101 0 0 0 1 1 00011 0 1 0 1 1 01011 0 0 1 1 1 00111 0 1 1 1 1 01111 1 0 0 0 1 10001 1 1 0 0 1 11001 1 0 1 0 1 10101 1 1 1 0 1 11101 1 0 0 1 1 10011 1 1 0 1 1 11011 1 0 1 1 1 10111 1 1 1 1 1 11111

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