Work out all the questions and give a detailed explanation on each please and thank you

1. What is the largest 10-bit binary number that can be represented with a. unsigned numbers? b. two's complement numbers? c. sign/magnitude numbers? 2. Convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Indicate whether or not the sum overflows a 6-bit result. a. 410+1910 b. 310+3210 3. Consider the Boolean function Y(A,B,C), represented by the truth table below. Implement Y using: a. an 8:1 multiplexer b. a 4:1 multiplexer and one inverter c. a 2:1 multiplexer and other logic gates 4. Complete the timing diagram of the circuits shown below. When clrn =0 (low), the output Q is always =0. a. b. E is the enable for the D Latch. For the Flip flop, when clrn =0 (low), Q is 5. Consider the Boolean function Y(A,B,C,D), given by the truth table below. a. Find a minimized expression for Y(A,B,C,D). b. Sketch a combinatorial circuit for Y, using its simplified expression. 6. Construct a JK flip-flop using a T flip-flop and zero or more other logic gates. 7. (15 pts) Implement a 3-bit synchronous counter up using SR flip-flops. Such a counter has the following transition diagram: 000001010011100101110111 and back to 000