Question

Design a combinational circuit with three inputs, x, y, and z, and three outputs, A, B, and C. When the binary input represents any of the decimal digits 0, 1, or 3, the binary output should represent the decimal digit that is two greater than the input, that is 2, 3, and respectively 5. Similarly, when the binary input represents any of the digits 5, or 6, the binary output should represent the digit that is three less than the input. The remaining three inputs, that are the binary representations of the decimal digits 2, 4, and 7 never Occur. Draw the truth tables, and give all minimal forms of the functions A, B, and C.

Answer 1

The design request by the student involves creating a truth table for a combinational circuit with specific output conditions and then determining the minimal forms for the functions A, B, and C to be implemented with logic gates.

Step-by-step explanation:

The student has asked for a design of a combinational circuit with three inputs (x, y, z) and three outputs (A, B, C) with specific output criteria based on decimal inputs. The conditions provided imply a need for a truth table to assess the behavior of this circuit for each triplet of inputs (x, y, z) representing the binary equivalents of the decimal numbers 0, 1, 3, 5, and 6.

Since the inputs 2, 4, and 7 never occur, their outputs can be treated as 'don't care' conditions during minimization.

The truth table for the valid inputs is as follows, with binary outputs that translate to the required decimal adjustments:

• (000) -> (010) : 0 -> 2
• (001) -> (011) : 1 -> 3
• (011) -> (101) : 3 -> 5
• (101) -> (010) : 5 -> 2
• (110) -> (011) : 6 -> 3

To minimize the functions A, B, and C, we can use Karnaugh maps or boolean algebra based on the truth table's outputs. This process will lead to the minimal forms of the functions for A, B, and C, which could be implemented by the student using logic gates like AND, OR, and NOT.