# the product of A x B represented as a 8 bit 2’s Complement number

**INSTRUCTIONS TO CANDIDATES**
###### ANSWER ALL QUESTIONS

4 bit 2’s Complement Multiplier

INPUT A: 4 bit 2’s Complement number

INPUT B: 4 bit 2’s Complement number

OUTPUT: the product of A x B represented as a 8 bit 2’s Complement number

You are only allowed to use the basic gates: NOT, AND, OR, XOR. You may however, use these basic gates to build your own custom circuits (i.e. Adder). You are NOT ALLOWED to use Logisim’s built in circuits. Each custom circuit is to be implemented as a sub-circuit as discussed in class.

PART 1: Build a 4 bit controlled 2’s Complement Inverter as a subcircuit named 4BitInverter

PART 2: Build a 8 bit controlled 2’s Complement Inverter as a subcircuit named 8BitInverter

PART 3: Build a 4 Bit UNSIGNED Multiplier as a subcircuit named UnsignedMultiplier

PART 4: Using the 3 subcircuits you built in Parts 1-3, built a 4 bit 2’s Complement multiplier that uses the inversion method discussed in class. Name this circuit: SignedMultiplier

HINTS: INVERSION METHOD:

1) If input A is negative, invert it. If input A is positive, leave it alone.

2) If input B is negative, invert it. If input B is positive, leave it alone.

3) Multiply A and B.

4) If both A and B originally had the same sign (both positive or both negative), do nothing.

5) If A and B originally had different signs (one was positive, the other negative), invert the product.

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