Convert the following expression into (i) Minimized Sum of Products (ii) Minimized Products of Sum (iii) Implement minimized POS with NAND Gates. F(D,C,B,A) = (A+B+C) (A'+B+D°) (A'+D) (B²+C') (B+C+D°)
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- Simplify the following expressions, and implement them with two-level NAND gate circuits: (a) AB'+ABD + ABD’+A’C’D'+A’BC' (b) BD + BCD'+AB’C’D' Draw a logic diagram using only two-input NAND gates to implement the following expression: (AB + A’B') (CD'+C°D)An equation in reduced SOP form, is F=AB+B'C+A'C'. I need to draw a logic circuit F using NOT/AND/OR and logoc circuit F using all NAND gates. Thank you for the help. I understood the previous types of gates but I am confused on how to draw these circuits.DISCUSSION: 1- Design the logic eircuit for the following conditions and draw the output wave form, X is a 0 if any two of the three variables A, B, and C are 1, X is al for all other conditions. 2- Implement the following function with only AND and NOT gates, F-AB+AB+BC W-XY (XZ+XY Z+ Y Z) + XZ 3- Use NAND gate, NOR gate, or combinations of both to implement the following expression:- a) X-A [B + C (D +E)] b) X B (CDE+EF G) (A B+ C) 4-a) What is the applications of AND gate and OR gate? b) In OR gate why 1 +1 1? c) The Fig. (1-12 ) shows the A & B inputs and the output is C, For the OR gate using the A and B inputs of Fig. (1-12) draw the C output for each of the following: The AND gate. • The NAND gate. • The NOR gate. .The EX-OR gate. • The EX-NOR gate. 1-12
- EXERCISES 1. Construct various basic logic gates with CMOS NAND gate. 2. If one of the two inputs of a NAND gate is connected to "1", it will act as a NOT gate. What happens if one input is connected to "0"? MULTIPLE CHOICE QUESTIONS () 1. The output F of a NAND gate is equal to: 1. A+B 2. AB 3. A+B ( ) 2. Which of the followings can be used to construct a NOT gate? ( )3. is equivalent to which of the followings? 2-11Simplify the expression G = (X’ + Y + Z’) (W + X + Y + Z) (W’ + X’ + Y’) using K- map and draw the corresponding simplified logic gate circuit.- The proportional distribution of A, B, C, D signals is given in the table as a percentage. It “logic 1” when the signals are accepted as active, “logic 0” when they are accepted as passive. takes. - When the proportional sum of active signals is over 50%, its output is "logic1", When we accept "logic 0" when it is below 50%, the output in the table Find the values. - Create an X function based on the logic values you find. Simplify the created X function. - Design the simplified function with NAND and NOR gates. - Set up the circuits you designed with NAND and NOR gates and observe the outputs. Show the output values by drawing a table, applying all possibilities to the input values.
- - The proportional distribution of A, B, C, D signals is given in the table as a percentage. It “logic 1” when the signals are accepted as active, “logic 0” when they are accepted as passive. takes. - When the proportional sum of active signals is over 50%, its output is "logic1", When we accept "logic 0" when it is below 50%, the output in the table Find the values. - Create an X function based on the logic values you find. Simplify the created X function. - Design the simplified function with NAND and NOR gates.Construct a circuit diagram that checks whether the two numbers A and B are in the ratio of 2:3. Also, derive the final Boolean equation for the function. F = 1 if A: B = 2: 3,0 otherwise Here, A and B both are 3 bit binary numbers. NB: You cannot use the IC of comparator, meaning for the comparison part, you need to draw the gate level diagram. You can use block level diagrams for the rest of the parts.T: Answer thne f. questions: 1) The hexadecimal number ´Al' has the decimal value equivalent to (A) 80 (B) 161 (C) 100 (D) 101 2) The output of a logic gate is 0 when all its inputs are logic 1. The logic is either (A) a NAND or an EX-OR (B) an OR or an EX-NOR (C) an AND or an EX-OR (D) an NOR or an EX-NOR 3) The Gray code of the Binary number 1100111 is (A) 1011011 (B) 1010100 (C) 1001001 (D) 101101 4) When simplified with Boollean Algebra (a+b)(a+c) simplifies to (A) a (B) a+a(b+c) (C) a(1+bc) (D) a+bc 5) -31 is represented as a sign Binary number ( using Sign-magnitude form ) equal to (A) 00011111 (B) 10101001 (C) 01110010 (D) 00101101 6) The Binary number 110111 is equivalent to decimal number (A) 25 (B) 55 (C) 26 (D) 34 7) With 4 bit, what the range of decimal values if the number is 2's complement signed number. (A) -32 to +31 (B) -2 to +1 (C) -8 to +7 (D) None of these
- In this problem we'll explore the fact that all logical circuits can be implemented using just NAND gates. The figure below shows you the symbol for a NAND gate and its truth table. We then show you how NAND gates can be wired together to perform the equivalent of a NOT gate, an AND gate, and an OR gate. NAND gate AB Output 1 01 1 Inputa Inputg Output 10 1 11 NOT A- AND D B. A. OR B. 2 i. Let's denote p NAND q as pīq. Write a logical expression for the thrce circuits corresponding to AND, OR, and NOT. ii. Validate your three logical expressions with three truth tables. For clarity and full credit, show cach variable and distinct sub-clause in a separate column, culminating in your final formula. 3. 2.Q1: Design and implement an asynchronous counter that counts from 0000 up to 1100 (modulus 13). Use OR gate, and show in the drawing how the OR gate is connected to truncate the state 1101.Please solve following problem on below: Simplify the following Boolean functions and draw the circuit with only NAND gates? a. F = AC’ + ACE + ACE’ + A’CD’ + A’D’E’ b. F = (B’+D’)(A’+C’+D)(A+B’+C’+D)(A’+B+C’+D’) Using DeMorgans theorem: c. F = (AB + A’B’)(CD’ + C’D) using only two input NAND gates?