Don't-Care Conditions in Canonical SOP
Binary-coded decimal (BCD) systems represent decimal digits using four-bit binary values, leaving six potential states unused in actual hardware.
A BCD digit detector takes a four-bit input consisting of A, B, C, and D, representing a value from decimal 0 to 15. The circuit drives an output Y high when the input is decimal 0, 1, or 2. Inputs representing decimal 10 through 15 will never occur in normal operation.
Determine the canonical Sum of Products (SOP) expression for Y using sigma minterm notation and identify how the unused states impact the final logic implementation.
Constraints
- Inputs are labeled
A,B,C,DwhereAis the most significant bit. - The output
Yis strictly 1 for decimal 0, 1, and 2. - The output
Yis strictly 0 for all other valid BCD inputs. - The output
Yis undefined for inputs 10 through 15.
Topics
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