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Course: DigitalLogic Design
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- a) Create a 4 Variable Karnaugh Map in paper by mapping 1’s for given standard SOP Boolean expression. After mapping , make relevant groups within Karnaugh Map by considering rules for making groups for 4 variable Karnaugh Map. After making relevant grouping , extract the minimum SOP expression by considering rules for extracting minimum SOP using Karnaugh Map. * Standard SOP: *Create Circuit Diagram using logic gates and logic converter in Multisim for given standard SOP and minimum SOP which you have solved. Do make sure that truth table for both expressions should evaluate same result.parity generator design, construct and test a circuit that generates an even parity bit ffrom four messages bits . use XOR gates. adding one more XOR gate, expand the circuit so that it generates an odd parity bit also.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.
- Using Boolean algebra theorems, simplify the logic expression above as far as possible. Create a Circuit Diagram for the new expression Then create a truthtable for the simplified circuitDesign a binary multiplier that multiplies two 8-bit binary number by following design rules thatshown in class. The Q and B are the two separate 8-bit binary inputs, C is the 3-bit sequence counterand R is the 16-bit result. (Note: Explain the registers that you will use to establish given process.) The steps are writing algorithm Drawing circuit undetailed (Just use the box, which have only writin under that their functions) Draw logic circuits one by one showing the internal structure of the boxes. Mahe flow chards for registersQuestion 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.)
- Derive the circuits for a three-bit parity generator and a four-bit parity checker using an odd-parity bit.A Boolean function simplified by using K-map in more simple than the sum of minterms standard form. True FalseGrey converters are often used in industrial circuits where the normal sequence of binary numbers may produce ambiguity during transition. This is elliminated with the Grey code, as only one bit changes, during a normal transition of sequential numbers. Show the logic required to convert a 10-bit binary number to Gray code and use that logic to convert the following to Gray code: a) 1010101010 b) 1111100000 c) 0000001110 d) 1111111111
- 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.A digital circuit for adding two binary digits has two inputs: the two digits to be added; and two outputs: the units bit and the twos bit of the answer. (a circuit of this kind is called half adder.) By treating this as two circuits, each with a single output, use Karnaugh maps to obtain a Boolean expression for each circuit, and draw the corresponding circuit diagrams.A synchronous counter counts through 3-bit prime numbers downwards. Assume the (b) counter starts with initial prime value set to 010 as its first 3-bit prime number. The undesired states will go with their next state to be don't cares. (i) Draw the state transition diagram of a state machine. (ii) Build the excitation table for the state machine. (iii) Find the simplest Boolean expression for the circuit using Karnaugh map. (iv) Implement the circuit diagram with implementation of JK flip flops and logic gates.