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An N-bit carry lookahead adder, where N is a multiple of 4, employs ICs 74181 (4 bit ALU) and 74182 ( 4 bit carry lookahead generator).
The minimum addition time using the best architecture for this adder is
The minimum addition time using the best architecture for this adder is
- a)proportional to N
- b)proportional to log N
- c)a constant
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An N-bit carry lookahead adder, where N is a multiple of 4, employs IC...
For N = 64 bits
Suppose you want to build a 64 bit adder then you need 16 4-bit ALU and 16 4-bit carry generator, at this point there will be 16 carries that will ripple through these 16 ALU modules, to speed up the adder we need to get rid of these 16 rippling carries, now we can again use 4 4-bit carry generator to generate these 16 carries, now we have only 4 carries to ripple through, again we can use the same trick to minimize the rippling of these 4 carries, we can use an additional 4-bit carry generator which will generate these carry and we are done :) there will be no more propagation of carry among the ALU modules.
So the we have used 3 level of 4-bit carry generator, and the time taken to add 64 bits will be proportional to 3 which is log464.
So in general to add N-bits it takes Log4N time.
Suppose you want to build a 64 bit adder then you need 16 4-bit ALU and 16 4-bit carry generator, at this point there will be 16 carries that will ripple through these 16 ALU modules, to speed up the adder we need to get rid of these 16 rippling carries, now we can again use 4 4-bit carry generator to generate these 16 carries, now we have only 4 carries to ripple through, again we can use the same trick to minimize the rippling of these 4 carries, we can use an additional 4-bit carry generator which will generate these carry and we are done :) there will be no more propagation of carry among the ALU modules.
So the we have used 3 level of 4-bit carry generator, and the time taken to add 64 bits will be proportional to 3 which is log464.
So in general to add N-bits it takes Log4N time.
Most Upvoted Answer
An N-bit carry lookahead adder, where N is a multiple of 4, employs IC...
Explanation:
To understand why the minimum addition time of an N-bit carry lookahead adder is proportional to log N, let's first understand the working of a carry lookahead adder and its components.
Carry Lookahead Adder:
A carry lookahead adder is a type of adder that reduces the propagation delay associated with the carry propagation in a ripple carry adder. It uses a carry lookahead generator to calculate the carry signals for each bit position in parallel.
74181 4-bit ALU:
The 74181 is a 4-bit Arithmetic Logic Unit (ALU) integrated circuit (IC) that performs various arithmetic and logical operations on 4-bit inputs. It has multiple modes of operation, including addition, subtraction, logical AND, logical OR, etc.
74182 4-bit Carry Lookahead Generator:
The 74182 is a 4-bit Carry Lookahead Generator IC that generates the carry signals for each bit position of a 4-bit adder in parallel. It takes the input carry and the input signals and produces the carry signals for each bit position.
Minimum Addition Time:
The minimum addition time of an N-bit carry lookahead adder is the time required to perform the addition operation with the least possible delay.
Proportional to log N:
The minimum addition time of an N-bit carry lookahead adder is proportional to log N.
- As N is a multiple of 4, let's consider N = 4M, where M is an integer.
- The carry lookahead generator 74182 generates the carry signals for each bit position in parallel.
- The carry lookahead generator IC has a delay associated with it, which is logarithmic in nature.
- The delay of the carry lookahead generator increases logarithmically with the number of bits.
- As the number of bits increases, the delay increases logarithmically, resulting in a proportional relationship with log N.
Therefore, the minimum addition time of an N-bit carry lookahead adder is proportional to log N.
To understand why the minimum addition time of an N-bit carry lookahead adder is proportional to log N, let's first understand the working of a carry lookahead adder and its components.
Carry Lookahead Adder:
A carry lookahead adder is a type of adder that reduces the propagation delay associated with the carry propagation in a ripple carry adder. It uses a carry lookahead generator to calculate the carry signals for each bit position in parallel.
74181 4-bit ALU:
The 74181 is a 4-bit Arithmetic Logic Unit (ALU) integrated circuit (IC) that performs various arithmetic and logical operations on 4-bit inputs. It has multiple modes of operation, including addition, subtraction, logical AND, logical OR, etc.
74182 4-bit Carry Lookahead Generator:
The 74182 is a 4-bit Carry Lookahead Generator IC that generates the carry signals for each bit position of a 4-bit adder in parallel. It takes the input carry and the input signals and produces the carry signals for each bit position.
Minimum Addition Time:
The minimum addition time of an N-bit carry lookahead adder is the time required to perform the addition operation with the least possible delay.
Proportional to log N:
The minimum addition time of an N-bit carry lookahead adder is proportional to log N.
- As N is a multiple of 4, let's consider N = 4M, where M is an integer.
- The carry lookahead generator 74182 generates the carry signals for each bit position in parallel.
- The carry lookahead generator IC has a delay associated with it, which is logarithmic in nature.
- The delay of the carry lookahead generator increases logarithmically with the number of bits.
- As the number of bits increases, the delay increases logarithmically, resulting in a proportional relationship with log N.
Therefore, the minimum addition time of an N-bit carry lookahead adder is proportional to log N.
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An N-bit carry lookahead adder, where N is a multiple of 4, employs ICs 74181 (4 bit ALU) and 74182 ( 4 bit carry lookahead generator).The minimum addition time using the best architecture for this adder isa)proportional to Nb)proportional to log Nc)a constantd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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