Question

after 53 clock pulses, what will be the state of the leds (on/off)? 1100 1011 0101 1010

Explanation:

Step1: Consider D - flip - flop operation

In a D - flip - flop based shift - register (which this appears to be), the state of the register changes with each clock pulse. The initial state of the LEDs can be considered as a binary number. Here, it seems the initial state of the 4 - bit register (LED1 - LED4) is 0101 (assuming OFF = 0 and ON = 1).

Step2: Use modular arithmetic for shift - register state

Since we have 4 D - flip - flops, the state of the register repeats after \(2^4=16\) clock pulses. We find the remainder when the number of clock pulses (53) is divided by 16. \(53\div16 = 3\) with a remainder of 5.

Step3: Shift the initial state 5 times

Starting with the initial state 0101, we shift it 5 times. After the first shift: 1010, second shift: 0101, third shift: 1010, fourth shift: 0101, fifth shift: 1011.

Answer:

1011