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Minimum number of Half adders, Full adders, AND gates required to implement 2 × 3 multiplier is given as
- a)1, 2, 6
- b)1, 1, 6
- c)2, 2, 6
- d)2, 1, 6
Correct answer is option 'D'. Can you explain this answer?
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Minimum number of Half adders, Full adders, AND gates required to impl...
Explanation:
Multiplier
- A multiplier is a combinational logic circuit that we use to multiply binary digits.
- We use a multiplier in several digital signal processing applications.
- We use it to design calculators, mobiles, processors, and digital image processors.
Process
- The first product obtained from multiplying A0 with the multiplicand is called as partial product 1.
- And the second product obtained from multiplying A1 with the multiplicand is known as the partial product 2.
The structure of multiplication is explained below:
There are 6 product terms so to get all those 6 AND gates are required.
There are 6 product terms so to get all those 6 AND gates are required.
To get the addition of B1A0 and B0A1 we require one-half adder and this produces a carry also.
To get the addition of B2A0, B1A1 and C1 we require Full adder because of 3 inputs and this also produces a carry.
To get the B2A1 and C2 we require one-half adder because of 2 inputs.
Conclusion:
Total 6 AND gates, 2 Half adders and 1 Full adder are required.
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Minimum number of Half adders, Full adders, AND gates required to impl...
To implement a 2-bit adder, we need to add two 2-bit numbers. This requires adding two pairs of bits, as well as carrying any overflow from the previous bit.
To add two bits, we can use a half adder. A half adder takes two inputs and produces a sum and a carry output. So, to add two pairs of bits, we need two half adders.
For the overflow bit, we need to add the carry output from the first half adder to the third input bit. This can be done with another half adder.
Therefore, we need a total of 3 half adders to implement a 2-bit adder.
In addition to the half adders, we also need AND gates to generate the carry inputs for the second and third half adders. Each half adder requires one carry input, so we need two AND gates to generate these inputs.
Therefore, the minimum number of half adders and AND gates required to implement a 2-bit adder is 3 half adders and 2 AND gates.
To add two bits, we can use a half adder. A half adder takes two inputs and produces a sum and a carry output. So, to add two pairs of bits, we need two half adders.
For the overflow bit, we need to add the carry output from the first half adder to the third input bit. This can be done with another half adder.
Therefore, we need a total of 3 half adders to implement a 2-bit adder.
In addition to the half adders, we also need AND gates to generate the carry inputs for the second and third half adders. Each half adder requires one carry input, so we need two AND gates to generate these inputs.
Therefore, the minimum number of half adders and AND gates required to implement a 2-bit adder is 3 half adders and 2 AND gates.
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Minimum number of Half adders, Full adders, AND gates required to implement 2 × 3 multiplier is given asa)1, 2, 6b)1, 1, 6c)2, 2, 6d)2, 1, 6Correct answer is option 'D'. Can you explain this answer?
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