If the binary strings are always 32 characters (i.e., leading zeros as needed), then
A B 201111110001111010000011101010001 2117928785 311001111111111110101111011001010 3489619658 410010100101100000110101100101111 2494589743 500110101010000101000011110110010 893552562 610100011010110100110000101110000 2740609392 711100001100101100010000111011111 3784712671 801110100011011101100111101010011 1953419091 900101011111000101101010101000010 736286018 1011111110111101100100000111001001 4277551561 1101111011000110101111110010101111 2065366191 1201100010100100110110011010111011 1653827259
The formula in B1 is
=SUMPRODUCT(MID(A2, {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}, 1)
* 2^{31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0})
If they vary in length,
A B 211100100101 1829 3110100000100110 26662 4100001101111000010001 1105425 5111011011001110111010110 15572438 61001011110100000010110100 19873972 71101111110000 7152
=SUMPRODUCT(MID(RIGHT(REPT(0,31) & A2, 32),
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}, 1) *
2^{31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0})
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