Consider a sequential digital circuit consisting of T flip-flops and D flip-flops as shown. At the beginning, \(Q_1=0\), \(Q_2=1\), \(Q_3=1\). Which one of the given values of \((Q_1,Q_2,Q_3)\) can NEVER be obtained with this circuit?
Consider a sequential digital circuit consisting of T flip-flops and D flip-flops as shown. At the beginning, \(Q_1=0\), \(Q_2=1\), \(Q_3=1\). Which one of the given values of \((Q_1,Q_2,Q_3)\) can NEVER be obtained with this circuit?
Show Hint
- \((0,0,1)\)
- \((1,0,0)\)
- \((1,0,1)\)
- \((1,1,1)\)
The Correct Option is A
Solution and Explanation
To solve this problem, we need to analyze the behavior of the sequential circuit consisting of T flip-flops and D flip-flops. Initially, the states are \(Q_1=0\), \(Q_2=1\), and \(Q_3=1\).
Let's go through the circuit:
- T Flip-flop: A T flip-flop toggles its output on every clock pulse if the input is high (1). If the input is low (0), the output doesn't change.
- D Flip-flop: A D flip-flop transfers its input directly to the output on the clock pulse.
- Initial State: Given \(Q_1=0\), \(Q_2=1\), and \(Q_3=1\).
Next, we evaluate the possible state transitions based on the initial configuration:
- Initially, \(Q_1 = 0\). With the first T flip-flop, if toggled by a clock pulse, \(Q_1\) changes to 1.
- Given \(Q_2 = 1\), passed via D flip-flop, allows \(Q_2\) to stay the same or change based on external inputs.
- The second T flip-flop toggles \(Q_3 = 1\) to 0.
Let's evaluate the options:
- (0,0,1) cannot be achieved since \(Q_3\) would toggle to 0 when \(Q_2\) = 1, which would result in (0,0,0) instead.
- (1,0,0) is achievable by toggling \(Q_1\) from 0 to 1, maintaining \(Q_2\) at 0, and toggling \(Q_3\) from 1 to 0.
- (1,0,1) can be obtained if \(Q_1\) and \(Q_3\) toggle with \(Q_2\) = 0 simultaneously.
- (1,1,1) is achievable by toggling both T flip-flops back to 1s, while \(Q_2\) remains 1.
Therefore, the state (0,0,1) can NEVER be obtained with this circuit configuration. This result is in line with the behavior of T and D flip-flops under the applied conditions.
Top Questions on Digital Logic
- What is meant by factoring?
- The simultaneous equations on the Boolean variables x, y, z, and w are: x + y + z = 1, xy = 0, x + y + w = 1, xy + z = 0. The solution for x, y, z, and w, respectively, is:
- Which of the following statements are not true?
- An FPGA with an embedded logic function that cannot be programmed is said to be:
- Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in GATE CS exam
A database has 25,000 fixed-length records of 100 bytes (primary key 15 bytes). The data file is block-aligned so each record is fully contained within a block. The file is indexed by a primary index file, also block-aligned and ordered. Block size is 1024 bytes and a block pointer is 5 bytes. Each index entry stores the block’s anchor key (15 bytes) and a pointer (5 bytes). Binary search on an index file of \(b\) blocks needs \(\lceil \log_2 b \rceil\) block accesses in the worst case. Given a key, the number of block accesses required to identify the data file block that may contain the record, in the worst case, is ____________.
- GATE CS - 2023
- Database Management Systems