A) Express the decimal number (- 30 ) as an 8-bit number in 2's complement form, and verifying its decimal value. B) Implement the Boolean function X = CD + CD + ABD using only NAND gates.
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- 3. Logic Design a. Create the truth table of a 3-input AND gate. Realize the 3-input AND operation using only 2-input NOR gates. b. Create the truth table of a 3-input OR gate. Realize the 3-input OR operation using only 2- input NAND gates. c. Using AND and OR logic gates, implement the logic function: F(x, y, z) = xy + yz + zx d. Using NAND logic gates, implement the logic function: F(x, y, z) = xy + yz + zxa) For the given logic circuit diagram write the program by using the gate level modeling. b) For the given truth table write the program by using the data flow Modelling. c) Write the test bench of the given logic circuit with all possibilities Y1 Y2 Y3 Y4 Y5 Y6 Y7 A2 A1 A0Implement the Logic expression using only NOT and two-input NAND gates. A+B+C+D
- How to build this circuit? (on Digital or Logisim) Binary-coded decimal is an alternative method of representing integers using binary. In it, each base-10 digit is represented by four bits, thus each nibble takes one of 10 values (0000 through 1001). Therefore, using BCD, 42 (decimal) is represented as 0100 0010 (binary) and 196 (decimal) is represented as 0001 1001 0110 (binary). Create a circuit in Logisim that accepts as input a pair of two-digit integers represented as BCD and outputs their sum in BCD. Any and all Digital components are fair game. You can assume that all inputs will be valid BCD-encoded numbers.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.1. a. i. Draw the gates required to build a half adder are ii. When simplified with Boolean Algebra (x + y)(x + z) simplifies to : iii. The output of a logic gate is 1 when all its inputs are at logic 0, the gate is either :
- 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.Minimize the Boolean expression F=AB’C’+C’D+BD’+A’C using K -map and implement the logic circuit using NAND gates only.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
- 4. A combinational logic circuit that compares between two 2-bit numbers A (AI A0) and B (B1 B0) is designed. Output F is high when A > B and low when A < B. a. Are there any conditions which cause none of the outputs to be asserted? If the conditions exist, what are the inputs? b. Derive the truth table and obtain the maxterm notation for the output. c. Obtain the minimized POS expression of the logic circuit. d. Draw the logic circuit using basic gates.2. The Boolean Algebra expression is given as Q = Ā(BC + BC + BC) + ABC a. Convert this logical equation into an equivalent SOP term. b. Use a truth table to show all the possible combinations of input conditions that will produce the output Q. c. Draw a logic gate diagram for the expression. d. Simplify the expression Q using Boolean Algebra. e. Draw the logic gate diagram of the simplified output Q.Question 3: a) Design a circuit which will add a 4-bit binary number to a 5-bit binary number. Use five full adders. Assume negative numbers are represented in 2's complement. (Hint: How do you make a 4-bit binary number into a 5-bit binary number, without making a negative number positive or a positive number negative?) b) A half adder is a circuit that adds two bits to give a sum and a carry. Give the truth table for a half adder, and design the circuit using only two gates. Then design a circuit which will find the 2's complement of a 4-bit binary number. Use four half adders and any additional gates. (Hint: Recall that one way to find the 2's complement of a binary number is to complement all bits, and then add 1.)