What the ALU Does

• Brawn of the CPU: Executes arithmetic (add, subtract) and logic (AND, OR, etc.).
• LEGv8 is 64 bits → need a 64-bit-wide ALU built from 64 identical 1-bit ALU “slices.”

Building Block 1: 1-Bit Logical Unit

• AND gate and OR gate compute a AND b and a OR b.
• A multiplexor chooses which operation’s result is output based on a control signal Operation.
• Result = (Operation=0 → AND) or (Operation=1 → OR).

Building Block 2: 1-Bit Full Adder

• Inputs: a, b, CarryIn.

• Outputs: Sum, CarryOut.

• Called a (3,2) adder. A half-adder would only have a and b as inputs.

• CarryOut equation (simplified):

  CarryOut = (a & b) | (a & CarryIn) | (b & CarryIn)

  (3 AND gates feeding one OR gate).

• Sum equation: XOR of all three inputs (true when exactly one or all three are 1).

Building Block 3: 1-Bit ALU (AND, OR, Add)

• Combine the 1-bit logical unit and the full adder.