The function f from the following circuit is equivalent to (' stands for bar or inverlted ihput). O x2x'3 + x'1x'2 + x'2X3 x'1x'3 + X2X3 + X'2X3 x'2X3
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- Design a circuit that takes three bits, X2, X1, X0 as input and produces one output, F. F is 1 if and only if 2<=X<=5 when X = (X2, X1, X0) is read as an unsigned integer. For example, if X2=1, X1=0, and X0=0, then the unsigned binary value is 100, which is 4, so the output would be 1. Your Assignment For This Problem Includes the Following Design the necessary circuit using Logisim to implement the situation described above. Use Kmaps for simplification. Be VERY careful to get the correct functions for your output before simplifying and designing the circuit with Logisim. You should minimize the circuit. Your circuit should have three inputs and one LED output. All inputs (X2, X1, X0) and output (F) should be labeled (in Logisim, not by hand). Please use these names to indicate the inputs and output so all projects are consistent. You should also include your name as a label on the circuit. Test your circuit to be sure it is working correctly.1. Design a 16*1 MUX using 4 *1 MUXs. 2. Design a 4-bit ALU to perform the following functions:A + B, A - B, A + 1, A’ . B’ ,A OR B, A XOR B, A AND B 3. Design a combinational logic that compares X and Y, where X = X1X0 and Y = Y1Y0; the output of combinational logic is 1, when X < Y; otherwise the output is 0.(a) Show truth table.(b) Find output function using K-map. 4. Design a logic circuit with three inputs and one output; the output generates even parity bit of the inputs.(a) Show the truth table. (b) Find output function. (c) Draw logic circuit.Design a circuit with a 4-bit BCD input A, B, C, D that produces an output W, X, Y, Z that is equal to the input + 3 in binary. For example, 9 (1001) + 3 (0011) = 12 (1100). The outputs for invalid BCD codes are don’t-cares. Write the truth table and the Karnaugh maps used to simplify the Boolean expression!
- Design a 2-bit comparator. The comparator input has two 2-bit numbers A and B. A consists of 2 bits a1 and a0. B consists of 2 bits b1 and b0. The comparator has three outputs Z2, Z1, Z0. a. Show the truth table for this comparator. b. Write the logic equation for Z2 that are true if only if A < B c. Write the logic equation for Z1 that are true if only if A > B d. Write the logic equation for Z0 that are true if only if A = B e. Show the logic design for this comparator using the minimum number of AND, OR, and Inverters. f. Verify your design using Logisim.Design a combinational logic circuit that takes a 3–bit input and has one output P. The P output should be active high only when the inputs corresponds to a prime number Note: the prime numbers: Prime numbers are 2, 3, 5, 7… Select one: a. P= AC+B b. P= A'C+A'B c. P= AC+A'B d. P= AC+A'B'28. Design a 2-bit comparator. The comparator input has two 2-bit numbers A and B. A consists of 2 bits a1 and a0. B consists of 2 bits b1 and b0. The comparator has three outputs Z2, Z1, Z0. a) Show the truth table for this comparator b) Write the logic equation for Z2 that are true if only if A < B c) Write the logic equation for Z1 that are true if only if A > B d) Write the logic equation for Z0 that are true if only if A = B e) Show the logic design for this comparator using the minimum number of AND, OR, and Inverters. f) Use Logisim to verify your design
- Using the truth table below ( An example sum-of-products expression is (A+B+C)(A+B+C')(A+B'+C)(A'+B+C).) a. Write a product-of-sums Boolean expression bexp4 for the output ? of the truth table b. Draw a circuit that is a direct translation of bexp4 without any simplification. For the circuit, use a layout that is analogous to the layout of the sample circuit below (where the and and or gates are appropriately swapped).1. DESIGN A COMBINATIONAL CIRCUIT THAT GENERATES THE 9'S COMPLEMENT OF A BCD DIGIT.2 DESING A COMBINATIONAL CIRCUIT THAT COMPARES TWO 4-BIT NUMBERS B AND C TO CHECK IF THEY ARE EQUAL. THE CIRCUIT HAS ONE OUTPUT, Z, SO THAT Z = 1 IF B = C AND Z = 0 IF B IS NOT EQUAL TO B.3. A COMBINATIONAL CIRCUIT IS DEFINED BY THE FOLLOWING THREE BOOLEAN FUNCTIONS. DESIGN THE CIRCUIT WITH A DECODER AND EXTERNAL GATES F1= X'Y'Z' + XZ F2= XY'Z' + X'Y F3= X'Y'Z + XY *HINT: OBTAIN THE KMAP AND TRUTH TABLEWe want to design a circuit that counts the number of 1s present on 3 binary inputs a, b, c and outputs that number in binary using 2 outputs y and z. For example an input of a=1, b=1, c=0 has two ones, so the output would be 210 = 102 i.e., y=1, z=0. a) Express y and z as sum of min‐terms of variables a, b and cb) Simplify the expressions for y and z using K maps.c) Draw the logical circuits for y and z using gates.
- Build a circuit that takes four bits as input: W, X, Y, Z. Treat WX as a 2-bit unsigned binary number, and treat YZ as a second 2-bit unsigned binary number. Your circuit should generate the output corresponding to the product of WX and YZ. You will need 4 bits of output for this problem.For example, if your input was 1011, your inputs correspond to 2 and 3. That product is 6, so your output will be 0110.Create a truth table for this problem, show all k-maps and minimizations, and build the corresponding (minimized) circuit. Use XOR, XNOR, NAND, and NOR as appropriate if it reduces the number of gates used.A sequential circuit is represented by the state equations and the output functions asgiven belowA(n+1) = C'x + A' BB(n+1) = B'(C+Ax')C(n+1) = ABx+B'xand y=BC+A'x z=ABx'+A'C where x is an external input and y and z are external outputs.a) Obtain the state table of the sequential circuit.b) Design the sequential circuit given above using JK flip-flops.Design the simplest circuit that has three inputs, a, b, and c, which returns an output value of 1 whenever g and b are complements of each other or b and c are complements of each other, otherwise the output is 0. Realize the circuit using 4input , 3output PAL