In this paper, the material implication logic gate has been realized using memristors. A memristor can be used as a logic gate or a latch which is known as `stateful logic' [8]. All logic gate realizations have been presented using material implication. A new realization of two carry lookahead adder architectures based on material implication has been proposed. A performance comparison with conventional ripple carry adder based on material implication has been performed.