1 Boolean Algebra and Logisim Task 0 0 0 10 0 0 1 1 01 0 1 0 011 0 1 0 1 11 0 1 1 001 0 1 1 01 1 10 0 1 1 Table 1: Truth table for Z1 and Z2 The main result of this task will be a logical circuit correctly implementing this Boolean function in the logisim simulator. Each step as defined in the following sub-tasks needs to be documented and explained. 1.1 Step 1: Boolean Algebra Expressions (8 points) Write the Boolean equation for your truth table in sum of products form. First, think about how to deal witlh the two outputs. Then, describe each single row in terms of Boolean algebra. Finally, combine the terms for single rows into larger terms. Briefly explain these steps for the truth table given 1.2 Step 2: Logical circuit in Logisim (8 points) Model the resulting Boolean terms from Step 1 in a single Logisim circuit, using the basic gates AND, OR, NOT. You can use gates with more than two inputs. Explain what you did for each step Test your circuit using values from the truth table and document the tests 1.3 Step 3: Optimized circuit (9 points) The goal of this task is to find a minimal circuit using only universal gates (NAND gates). Based on the truth table and Boolean algebra terms from Step 1, optimize the function using Karnaugh maps . You will need to create two Karnaugh maps, one for each output. Your documentation should show the maps as well as the groups found in the maps and how they relate to terms in the optimized Boolean function. (5 points) Then use Logisim to create a minimal circuit. Don't use any other gates than NAND. Test your optimized circuit using values from the truth table. (4 points)