13. Using the I/O table, construct the appropriate Boolean expression, in CDNF, and a circuit for that expression x y z f(x,y,z) 1 1 1 1 1100 1010 1000 0 1 1 0 0100 0010 0001
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- Expand each expression to a standard SOP form: (a) AB + ABC + ABC (b) A + BC (c) ABCD + ACD + BCD + ĀBCD (d) AB + AB CD + CD + BCD + ABCDDesign a clocked sequential circuit that recognizes the 4-bit input sequence 1010, including overlap such that for input x = 01010100011010010100 the corresponding output Z = 0000101000000100001. Design the circuit using D Flip-Flops. You have to show the following: i. The state diagram ii. The flip-flop input table iii. The simplified equation(s) for the flip-flop input(s) and the output(s) iv. The final circuit diagramGiven two 8-bit unsigned numbers, A and B:Using MSI components (comparators, multiplexers) design a circuit whose output X is as follows: X IF A <=B 2B IF A >B 2A
- Answer this question, part (1), (2) & (3). Design a combinational logic circuit that converts a three-bit binary number from code A to code B, according to the table on the right. Answer the following questions: Code A Code B 000 000 001 001 011 010 010 011 110 100 111 101 101 110 100 111 Construct the truth table for the circuit. Derive the Sum-of-Products (SoPs) Boolean expression for each of the circuit outputs. Using Boolean algebra, simplify the expression you obtained in Part 2 above.Use Karnaugh map to reduce the following Boolean expression then draw the digital circuits for the simplified expression. F= A’BC + ABC’ + A’B’C + A’B’C’ + A’BC’Design a combinational circuit that increments the 4-bit binary input. The output of the circuit is also represented as 4 bits. For example, if the input is 0011 then the output is 0100. Note: the increment of 1111 is 0000. Let the input variables be A, B, C, and D, while the output variables be W, X, Y, and Z. What is the boolean function (in sum of minterm format) of output W? What is the boolean function (in sum of minterm format) of output X? What is the boolean function (in sum of minterm format) of output Y? What is the boolean function (in sum of minterm format) of output Z?
- Given a 100-MHz clock signal, construct a circuit using T flip-flops to generate 50-MHz and 25-MHz clock signals.Design a truth table for a combinational circuit that detects an error in the representation of a decimal digit encoded in BCD. (This circuit should output a 1 when the input is one of the six unused combinations for BCD code.)Design a combinational circuit that detects an error in the representation of a decimal digit in BCD. In other words, the output is equal to 1 when the input contains any one of the six unused bit combinations in the BCD code. Using NAND Gates only. start with truth table.
- Design a circuit that will multiply BCD ( Binary Coded Deciamal code) numbers which are between 0-9 with 10 (ten). Use an inverting output (4-10) Decoder. (Note: if input is 3 in BCD, output must be 3x10=30 in BCD)Use Boolean algebra to find the simplified circuit below: F (A, B, C) = AB+A΄B΄C΄+A΄BC΄ Use a Karnaugh map to find the minimum (SOP) form for the expression: F (A, B, C) = AB+A΄B΄C΄+A΄BC΄Use a Karnaugh map to simplify the following standard SOP expression:XY'Z + XYZ' + X'YZ + X'YZ' + XY'Z' + XYZ