## Question

2) [10 marks] Using T Flip-Flops, implement a 3-bit register that does not change when external inputs xy = 00, shifts to the right by 1 when xy=01, = rotates to the right by 1 xy = 10, and counts by 5 when xy = 11. Show your State Table, K-maps as well as the sequential circuit diagram.

3) [10 marks] Implement a 3-bit binary counter that counts by 3 (modulo 8) using a D flip-flop for the most significant bit, an R-S flip-flop for the middle bit, and a T flip flop for the least significant bit. Show your State Table, K-maps as well as the sequential circuit diagram.

4) [10 marks] Consider the following combinational circuits:

(i) F1(x,y,z) =Σ(1,2,3,6)

F2(x,y,z) = Σ(0,3)

F3(x,y,z) = Σ(0,2,3,7)

(ii) F1(w,x,y,z) = Σ(0,4,6,9,11,12,14)

F2(w,x,y,2)= Σ(2,3,4,8,11,15)

F,(w,x,y,z)= Σ(0,2,11)

F1(w,x,y,z) = Σ (10, 11, 14,15)

a) Implement Part (i) using a ROM chip (be sure to specify the size).

b) Implement Part (ii) using a ROM chip (be sure to specify the size).

c) Implement Part (ii) using 8x3 ROM chips.

d) Implement Part (i) using a 16x4 ROM.

5) [10 marks] Consider a RAM chip with a capacity of 512K words of 8 bits each.

a) How many address and data lines are required for this chip?

b) How many 512K x 8 RAM chips would be required to construct an 2M x 16 RAM chip?

c) How many address and data lines are required for an 2M x 16 RAM chip?

d) What size decoder is needed to construct an 2M x 16 chip from 512K x 8 chips?

e) Draw a diagram of the 2M x 16 chip built from 512K x 8 chips. Include the range of addresses for each chip.

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