Final answer:
The gate design for a 2 bit multiplier that can handle signed binary is the sign-extended multiplier.
Step-by-step explanation:
The gate design for a 2 bit multiplier that can handle signed binary is the sign-extended multiplier.
This design uses two signed 2-bit numbers as input and produces a 4-bit signed result.
One approach to implementing this design is to use combinational logic to perform the multiplication and sign extension. The sign extension is done by duplicating the most significant bit of the multiplicand and the multiplier and appending them to the respective numbers.