## EEL 3705: Fundamental of Digital Circuit

1) A sequential circuit with two D flip-flops A and B, two inputs, x and y, and one output z is
specified by the following next-state and output equations: (10 point)
π΄π‘+1 = π₯π¦
β² + π₯π΅
π΅π‘+1 = π₯π΄ + π₯π΅
β²
π§ = π΄
a) Draw the logic diagram of the circuit.
b) List the state table for the sequential circuit.
c) Draw the corresponding state diagram.
2) A sequential circuit has two JK flip-flop A and B and one input x. The circuit is described by the
following flip-flop input equations: (15 point)
π½π΄ = π₯ πΎπ΄ = π΅
π½π΅ = π₯ πΎπ΅ = π΄
β²
a) Derive the state equations π΄π‘+1 and π΅π‘+1 by substituting the input equations for the J
and K variables.
b) Draw the state diagram of the circuit.
3) A sequential circuit has three flip-flops A, B, C; one
input πππ; and one output πππ’π‘. The state diagram is
shown in next figure. The circuit is to be designed by
treating the unused states as donβt care conditions.
Analyze the circuit obtained from the design to
determine the effect of unused states. (15 point)
a) Using D flip-flops
b) Using T flip-flops
4) Design a sequential circuit with two D flip-flops A
and B, and one input π₯ππ. (15 point)
a) When π₯ππ = 0, the state of the circuit remains the same. When π₯ππ = 1, the circuit goes
through the state transitions from ππ β ππ β ππ β ππ β ππ and repeats the
sequence.
b) When π₯ππ = 0, the state of the circuit remains the same. When π₯ππ = 1, the circuit
goes through the state transitions from ππ β ππ β ππ β ππ β ππ and repeats the
sequence.
5) Design a four-bitshift register with parallel load using D flip-flops. There are two control inputs:
shift and load. When shift = 1, the content of the register is shifted by one position. New data are
transferred into the register when load = 1 and shift = 0. If both control inputs are equal to 0, the
content of the register does not change. (10 point)
6) Draw the logic diagram: (15 point)
a) A four-bit register with four D flip-flops and four
4 Γ 1 multiplexers with mode selection inputs 1 and 0.
The register operates according to the following
function table.
b) A four-bit binary ripple countdown counter using
flip-flops that trigger on the positive-edge of the clock.
c) A timing circuit that provides an output signal that stays on for exactly twelve clock
cycles. A start signal sends the output to the 1 state, and after twelve clock cycles the
signal returns to o state.
7) Using D flip-flops: (20 point)
a) Design a counter with the following repeating binary sequence π β π β π β π β π.
Draw the logic diagram of the counter.
c) Design a counter with the following repeated binary sequence 0 β π β π β π β π.
Draw the logic diagram of the counter

Powered by WordPress