An AND logic operation rule capable of carrying out an AND logic operation between binary digits and an AND logic operation between multi-nary digits is defined and an AND logic device utilizing the AND logic operation is disclosed. The AND logic operator having three multi-nary logic inputs consists of two multi-nary AND logic operators having two inputs, respectively. The multi-nary AND logic operator carries out the function of the prior binary AND logic operation and the function of the binary-multi-nary AND logic operation.