CLA Delay

Question

A 4-bit carry lookahead adder, which adds two 4-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using two-level AND-OR logic. (A) 4 time units (B) 6 time units (C) 10 time units (D) 12 time units

Comments

https://gateoverflow.in/1057/gate2004_62

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can you provide any other detailed explanation as i have gone through many sites but i still do not get how propagation delay of CLA is calculated??

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offcourse i will ...explain u..if u have asked...wait for some time in the evening/night  i will upload detailed explanation

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ok..thankyou

Answer 1

i have tried best possible solution...

consider below diagram in which 'A' represents ;Akriti' & 'B' represnts 'Basmati'your friend 

                       

now akriti wants to meet her friend basmati who lives at certain distance (as mentioned in figure by a line)

now the time taken by akriti to reach basmati  (consider 1 minute) is called propgation delay.

now consider below figure in which A as akriti and  A1 as akriti1 lives at same place so is case with B basmati & B1 as basmati1

                                      

now assume both akriti & akriti1 want to meet respective basmati's  so they leave at same time and travel same distance...so the time taken by both will be 1 minute .

how 1minute  ..see individually they have travelled 1-1 minute respectively but we cannot take 2minutes as propogation delay...assume both left at 10:15 am and they reached at 10:16 so only 1 minute propogation delay...in that 1 minute either 1 akriti travels or 100 akriti travels  delay will be only 1 minute not 100 minutes ...same concept is used in question

now consider our question i m considering 1 of the way to draw look ahead carry adder there  may be other ways also but the carry generator is same as given in the question i.e is 2- level AND-OR 

there r 2 figures in above picture the right hand part called as look ahead carry generator is part of left hand figure that have to put inside blue box given///for clearer view i considered this picture.

now consider RHS part( generator's part) assume

if we give input to AND gate it gives output after 1 minute as there were 2 akriti's here 6 AND gates

i.e AND1,...AND6..so it will  take only 1 minute to give output by all  AND gates...( not 6 minutes )

and after that  output  is fed as a input to OR gate which again takes 1 minute to give output...same as AND gate ...to total 2 minutes time taken by the carry generator..

now take LHS figure in which 2 more levels are there...in first level

ex-0r & AND gates ,i.e x-0r1 & AND1.....ex-0r4 & AND4..will again take only 1minute to give output

and in last level ex-or gate same concept....... again will take 1 minute to give output ....so if we add all we get total 4 minutes of delay ....i.e 1min by first level ////2min by carry generator///1 min by last level

Comments

i will try...wait 4 sumtime

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ohkay..

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we are not provided XOR gates in the question..so answer should be 6 time units as xor is two level AND-0R .