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A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate.
The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4-bit-ripple-carry binary adder is implemented by using four full adders. The total propagation time of this 4-bit binary adder in microseconds is ______.
The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4-bit-ripple-carry binary adder is implemented by using four full adders. The total propagation time of this 4-bit binary adder in microseconds is ______.
Correct answer is '19.2'. Can you explain this answer?
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Calculation of Propagation Delay:
Calculation of Total Propagation Time for 4-bit Binary Adder:
Final Answer:
However, this is not the correct answer. We need to consider the fact that the carry signal has to ripple through each full adder. This means that each full adder will receive the carry signal from the previous full adder with a delay. Therefore, the actual propagation time will be more than 33.6 microseconds.
The carry signal has to ripple through four full adders. The maximum delay between any two bits is the propagation delay of one full adder plus the time taken for the carry signal to ripple through the previous full adder. Therefore, the total propagation time of the 4-bit binary adder is:
Total propagation time = (Propagation delay of one full adder + Ripple delay between full adders) x 4
The ripple delay between full adders is the time taken for the carry signal to ripple through one full adder. Since the carry signal has to ripple through two half adders and an OR gate in a full adder, the ripple delay is:
Ripple delay = Propagation delay of two half adders + Propagation delay of OR gate
= (Propagation delay of XOR gate + Propagation delay of AND gate) x 2 + Propagation delay of OR gate
= (2.4 microseconds + 1.2 microseconds) x 2 + 1.2 microseconds
= 7.2 microseconds
Therefore, the total propagation time of the 4-bit binary adder is:
Total propagation time = (8.4 microseconds + 7.2 microseconds) x 4
= 60.0 microseconds
Hence, the correct answer is 60.0 microseconds, which is equal to 4 x (2 x (2.4 microseconds + 1.2 microseconds) + 1.2 microseconds) = 4 x 19.2 microseconds.
- Propagation delay of XOR gate = 2 x propagation delay of AND/OR gate = 2 x 1.2 microseconds = 2.4 microseconds
- Propagation delay of half adder = propagation delay of XOR gate + propagation delay of AND gate = 2.4 microseconds + 1.2 microseconds = 3.6 microseconds
- Propagation delay of full adder = 2 x propagation delay of half adder + propagation delay of OR gate = 2 x 3.6 microseconds + 1.2 microseconds = 8.4 microseconds
Calculation of Total Propagation Time for 4-bit Binary Adder:
- 4-bit binary adder is implemented using four full adders.
- The maximum propagation delay between any two bits in the 4-bit binary adder is the propagation delay of one full adder.
- Therefore, the total propagation time of the 4-bit binary adder = propagation delay of one full adder x 4 = 8.4 microseconds x 4 = 33.6 microseconds
Final Answer:
- The total propagation time of the 4-bit binary adder in microseconds = 33.6 microseconds
However, this is not the correct answer. We need to consider the fact that the carry signal has to ripple through each full adder. This means that each full adder will receive the carry signal from the previous full adder with a delay. Therefore, the actual propagation time will be more than 33.6 microseconds.
The carry signal has to ripple through four full adders. The maximum delay between any two bits is the propagation delay of one full adder plus the time taken for the carry signal to ripple through the previous full adder. Therefore, the total propagation time of the 4-bit binary adder is:
Total propagation time = (Propagation delay of one full adder + Ripple delay between full adders) x 4
The ripple delay between full adders is the time taken for the carry signal to ripple through one full adder. Since the carry signal has to ripple through two half adders and an OR gate in a full adder, the ripple delay is:
Ripple delay = Propagation delay of two half adders + Propagation delay of OR gate
= (Propagation delay of XOR gate + Propagation delay of AND gate) x 2 + Propagation delay of OR gate
= (2.4 microseconds + 1.2 microseconds) x 2 + 1.2 microseconds
= 7.2 microseconds
Therefore, the total propagation time of the 4-bit binary adder is:
Total propagation time = (8.4 microseconds + 7.2 microseconds) x 4
= 60.0 microseconds
Hence, the correct answer is 60.0 microseconds, which is equal to 4 x (2 x (2.4 microseconds + 1.2 microseconds) + 1.2 microseconds) = 4 x 19.2 microseconds.
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A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate.The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4-bit-ripple-carry binary adder is implemented by using four full adders. The total propagation time of this 4-bit binary adder in microseconds is ______.Correct answer is '19.2'. Can you explain this answer?
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