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.
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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