49. Half Subtractor Design

• Output Difference Analysis: The Difference output turns on (1) whenever only one of the inputs is high (rows 01 and 10). This directly matches an exclusive-OR (XOR) gate behavior.
• Output Borrow Analysis: The Borrow output turns on (1) strictly when Minuend A is 0 and Subtrahend B is 1 (row 01). This requires inverting Minuend A and combining it with Subtrahend B using an AND gate.
• Hardware Optimization: Minuend A and Subtrahend B are routed in parallel. While both inputs connect directly to the XOR gate for the Difference output, Minuend A passes through a NOT gate before entering the AND gate with Subtrahend B to form the Borrow output.
• Boolean Equations:

Output Difference = Minuend A ^ Subtrahend B

Output Borrow = ~Minuend A . Subtrahend B