54. Signed Multiplier

Step 1: Sign Calculation

The circuit separates the sign bits from the value bits. The final sign bit (SignP) is determined by an XOR gate: if the input signs match, the result is positive (0); if they are different, the result is negative (1).

Step 2: Value Calculation

• MagP0 Output: This is the first column of the value math. It multiplies the lowest value bits (MagA0.MagB0) using a single AND gate.
• MagP1 Output: This bit adds the middle cross-multiplied terms (MagA1.MagB0 and MagA0.MagB1). An XOR gate finds the sum for MagP1, while any overflow into higher bits is dropped to fit the fixed 3-bit output limits.

Boolean Equations:

• SignP = SignA ^ SignB
• MagP1 = (MagA1 . MagB0) ^ (MagA0 . MagB1)
• MagP0 = MagA0 . MagB0