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Q1 (50 points)/ Consider the function f(x1,x2,3)= {m(0,3,4,6,7). a) Design the simplest sum-of-products that implements f....
Solve the following problems: 1.(4 points) Design the simplest sum-of-products circuit that implements the function Write the truth table, canonical SOP form, minimal form, and cost. 2.(4 points) Design the simplest product-of-sums circuit that implements the function f(x1, X2, X3 ) = II M(2,3,6). Write the truth table, canonical POS form, minimal form, and cost. 3.(2 point) Design a circuit that implements the simplest sum-of-products circuit that implements the function ing only NAND gates. Show all work, including logic networks.
Question 4 Design the simplest circuit that implements the function f(x7x2, x3) = m(1,3,5,7) using only NAND gates.
Consider the following function. (8 <A ri eve n of products) expression. Don't draw the gate 1131 0 diagram yet. (b) Use De Morgan's Laws or "bubble pushing" to convert the SOP expression to something that can be directly implemented with only NAND/NOR/inverter gates. (c) Now draw the schematic (logic gates) for the resulting NAND/NOR/inverter circuit.
Q2. [60 marks] A logical function is realized by the combination of NAND and NOR gates with the ircuit connections shown in Figure1. a. [20 points] Find the Boolean expression of the function F b. [20 points] Simplify the Boolean expression using Boolean Algebra; c. [20 points] Re-design the circuit using the least NAND-only gates (each NAND has 2 inputs). F(A,B,C) Figure 2: Logical circuit with NAND and NOR.
(1)Try to use NAND gates to achieve the truth table function of an XOR gate (2) Try to design a clicker for three people, it just needs two people to agree to pass. A,B,C indicate the people, 0 means don't agree, 1 means agree. If it passes the result is 1. Please write the truth table, the SOP (sum of products) equation and draw the logic circuit for it. (3)Use a Karnaugh-map to simplify the following Boolean function: F= AB'C'+A'B'C'+AB'C+A'B'C+AB...
6. (10 points) Given the following circuit diagram, please find out the corresponding logic expression F. Re-write the function F using the canonical sum-of-products representation (Note that the final answer needs to be a logic expression without using the m, M, or notations) NS
1. What logic gates are known as universal gates? (1 point) a) nand, nor b) and, or, not c) nand, nor, xor, xnor d) None of the above 2. Write the half adder truth table. (4 points) 3. Fill in the blank. (1 point) A2 to 1 mux has input lines. 4. True or False? (1 point) A Boolean algebraic sum of products expression is the complement of the product of sums expression. 5. What is the minimum POS expression...
DESIGN SECTION Before the experiment, you are going to design a circuit which has 4 inputs w, x, y, z and an output F. If 4-bits input value is “odd number which is higher than 4”, or “3-bits highest even number” or “4-bits highest even number”, the output function F will be equal to 1. Otherwise F=0. Each students have to design the circuit and have to do following steps own by own. You are going to; a) Fill the...
Implement the Boolean function F(w,x,y,z) = Σm(3, 4, 5, 1 1, 12, 13, 14, 15) using a minimum number of NAND gates only. Write the minimal logic expression (no need to draw the circuit).
Referring to the circuit in Figure 2 and the corresponding function table in Table 5 on page 5, answer the following questions: a) Draw the state diagram of the circuit (b) (5 Marks) Work out the logic circuit for the Output Block using only NAND gates and inverters. (5 Marks) (c) Give a brief description on the functional characteristics of the circuit in Figure 2 (2 Marks) (d) Redesign the circuit using only one flip-flop and some logic gates. You...