Consider the (7, 4) linear code whose parity-check matrix is 100 1011 Н- 010 1110 001 0111 a) Calculate the syndromes for the following error pattern e=0000001 (b) Determine the generator matrix (G c) Find the code word if the message m = 0011

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Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs. Check your answers by converting to decimal sign-and-magnitude representation. 00110110 01110101 11011111 + 01000101 + 11011110 + 10111000 00110110 01110101 11010011 - 00101011 11010110 - 11101100

4. EA sequence detector is to be designed to detect both the sequence 11 and 010 simultaneously. You will develop a state diagram with one input variable X and one output variable Z. The output is 1 if and only if the last two input bits are 11 or the last three bits are 010. Note that sequences may overlap. Sample input: 0010101111001101001 Sample output: 0001010111000100100 A) state with So and other states with S1, S2, S3, etc. Use a minimum number of states in Mealy model. Hint: please do NOT arrange all states in one line. Draw the state diagram. Label each arc with X/Z. Label the initial Start So B) Implement this state diagram using the minimum number of D flip- flops. Draw the state table for this state diagram. Assume that we use the following state assignments: So = 00; S1 = 01; S2 =10; S3 = 11. Qi Qo X Q1 (t+1) Qo (t+1) Z Complete the following three K maps. And then derive optimized C) Boolean expressions for the inputs to the D flip-flops and the output of the sequential…

Design and implement a 2-bit integer division circuit. The circuit has four inputs A1,A0,B1,B0 and five outputs Q1,Q0,R1,R0,E. The values on A1,A0,B1,and B0 are treated as unsigned binary integer number A and B respectively. The circuit should generate the quotient Q and remainder R of the division A/B on lines Q1,Q0,R1,R0 respectively. If division by zero is attempted, line E is set '1' otherwise E is '0' and the values on lines Q1,Q0,R1,R0 are considered invalid (If division by zero is attempted).  Document the following: 1.specify the truth table for the circuit 2.derive necessary boolean equations (kmaps) 3.draw gate-level logic diagram (logic gate symbols)

Develop a Truth Table for the following Muliplexerer

Two's compliment of binary number 101010 is 010110 001110 011110 010101