FIT 1047 Assignment 1 Part 1b

Part 1b Task 1.1

• SOP for Z1: Firstly we need to find the row that z1 = 1 and then construct the boolean expression:

• POS for Z1: Firstly we need to find the row that z1 = 0 and then construct the boolean expression:

• SOP for Z2:

• POS for Z2:

Part 1b Task 1.2

• A brief explanation of my construction:

1. Inputs: X1, X2, X3, and X4 are the input variables, which determine the outputs.

2. AND Gates: The AND gates are used to implement each term from the truth table. They take the inputs directly or their complements (through NOT gates).

3. OR Gates: The OR gates combine the terms generated by the AND gates to produce the final outputs Z1 and Z2.

• 3 test cases

1. Case 1 in screenshot:

1. Case 2 in screenshot

1. Case 3 in screenshot

Part 1b Task 1.3

• The K-map for Z1:

• The group

• The optimized Boolean functions

• The optimized minimal circuit

• Test of 3 cases

1. Case 1

1. Case 2

1. Case 3

• The K-map for Z2

• The group

• The optimized Boolean functions

• Test of 3 cases

• Case 1

• Case 2

• Case 3