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)
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- Logic Gates:* 7404LS (NOT)* 7408LS (AND)* 7432LS (OR)* 7400LS (NAND)* 7402LS (NOR)* 7486LS (EX-OR)Or you can use 74HCxx versions. Task 2: 4 INPUT PRIORITY ENCODERa) Write the truth table.b) Find the outputs in terms of min terms using minimal expression.c) By using K map, find the simple/simplest expression of theoutputs.d) Draw the circuit diagram. (Simulation design will be accepted.)e) Simulate the circuit & explain your results. (Please do notdesign separate simulations for each output. You should design ONEsimulation including all inputs and outputs.)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.)Assume that the exclusive-OR gate has a contamination delay of 3 ns and that the AND or OR gates have a contamination delay of 2 ns. What is the total contamination delay time in the 4-bit adder? Note: your answer should include only the value of the delay without the unit (only the number) Note: Submit your work on paper as well А- B- Cin- Cout Answer:
- DISCUSSION: 1- Is the Gray code arithmetic code? Why? Where this code usėd? 2- What is the parity bit? 13- Design five - bit odd parity checker? 4- a) What are the main applications of the comparator? /b) Design two – two bit comparator. -5- Convert five.bit Gray to binary code, write truth table and draw the circuit diagram. 2-51) What is the biggest binary number (decimal value) you can write with 6 bits? What is the biggest binary number (decimal value and in terms of n) you can write with n bits? If you want to represent the decimal numbers from 0-16, what is the minimum number of bits you will need? Convert the decimal number 238 to binary number. (ZERO point if not showing steps/calculation!)1. Gray code to Binary converter: Gray code is one of the codes used in digital systems. It has the advantage over binary numbers that only one bit in the code word changes when going from one number to the next. (See Table 1). Design a combinational circuit with 4 inputs and 4 outputs that converts a four- bit gray code number into an equivalent four-bit Binary number. Use Karnaugh map technique for simplification. Use LogicWorks for pre-lab demonstrations. Select the library "7400dev.clf* in the Parts Palette and then select the XOR chip 74-86. This would give you a set of 4 XOR's as shown in Fig. 1, just like the hardware chip 74-86. You could use as many as needed from these XOR gates in your design. Get back to ALL LIBRARIES and select switches for the inputs and Binary Probes as indicators of the outputs. Verify your design in the pre-Lab. During the Lab construct the circuit and verify its operations.
- 5. In the circuit implementation of an 8-bit adder, explain why the carry bit connection of the least- significant bit is connected to ground. Explain in words what values for A, B, C, D, E will cause a 1 to appear at point X. The circuit below uses a 5-input AND gate. Draw the equivalent circuit using only 2-input gates.1-Using the Karnaugh Method, design and draw the circuit of the logic circuit that gives the result of the multiplication of the two-bit numbers "AB" and "CD" according to minterms (SOP). Do not make any further simplifications before or after the Karnaugh Method. In tables and Karnaugh, ensure that the least significant bit is on the far right and the entries are sorted alphabetically. Make sure that the circuit you have drawn is understandable, the function you have written and the truth table are readable.12. Use 4-bit binary addition, perform -2 + 2. First convert the decimal numbers to signed 2's complement binary numbers. Circle the lower 4 bits of the answer. Is the 4-bit answer correct? There is a short cut to taking the 2's complement. You can flip every bit to the left of the right most one. Let's try it. (+3)10=(0011),. If we flip every bit to the left of the rightmost 1 (which is in bold and underlined) we’ll get (1101), which according to the table above is (-3)10! Let's try another. (-6),0 = (1010),. If we flip every bit to the left of the rightmost 1 (in bold and underlined) we'll get (0110), which is (+6)10- 13. (+20)10=010100. Take the 2's complement of 010100 by Taking the 1's complement and adding 1. b. Using the rightmost 1 shortcut. 14. Check your answer from part 13 a and b (they should be the same) by converting it to decimal. Since we are using a 6-bit representation, use a "(-32) 16 8 4 2 1" weighting.
- If we want to design a logic circuit that make selective complement for example, to complement the first two-bits of the number (1010) to become (1001) O using XOR gate with 0011 O using OR gate with 1100 O using XNOR gate with 1011 O using AND gate with 1100What parity bit, P, should be added to the following data if the parity is EVEN? If the parity is ODD? a. 1111100 b. 1010110 c. 00011014. Use the Word table tool to construct the truth table for this circuit. Be sure to include intermediate values. Insert column headings in the first row. Be sure to use the Insert > Equation tool so that standard Boolean logic symbols are displayed in the headings. A B. D In the circuit implementation of an 8-bit adder, explain why the carry bit connection of the least- significant bit is connected to ground. Explain in words what values for A, B, C, D, E will cause a 1 to appear at point X. A B E