55. 1-Bit ALU Slice

Step 1: Operation Selection

The circuit runs all four operations (AND, OR, XOR, and Addition) simultaneously. A multiplexer network uses the selection control lines (Op1, Op0) to choose exactly one of these computed values to pass forward as the final Result.

Step 2: Continuous Carry Calculation

The circuit calculates the carry-out (Cout) independently using standard full adder logic. Because it bypasses the selection switches, the carry signal stays continuously active, allowing multiple slices to be chained together for multi-bit addition.

Boolean Equations:

• And_Result = A . B
• Or_Result = A + B
• Xor_Result = A ^ B
• Add_Result = A ^ B ^ Cin
• Cout = (A . B) + (Cin . (A ^ B))
• Result = (And_Result . ~Op1 . ~Op0) + (Or_Result . ~Op1 . Op0) + (Xor_Result . Op1 . ~Op0) + (Add_Result . Op1 . Op0)