On the Condensing of Alpha-Bits

An advert for cereal? Count me in.

For those familiar with the original manual.

000000801000G10000O11000
100001901001H10001P11001
200010A01010I10010Q11010
300011B01011J10011R11011
400100C01100K10100S11100
500101D01101L10101T11101
600110E01110M10110U11110
700111F01111N10111V11111

X corresponds to the bit to the left of the operator used; Y corresponds to the bit to the right.

InputsDigits -> Operators
01234567
XYORANDXORIMPNORNANDXNORIMPBY
1111010011
1010100101
0110110100
0000011111