How do you compute and compare the delays between a (4:2) compressor and (3,2) counter carry save tree?

My question: How is Table 6.8 shown below computed for different operands? For example, for 3 operands how did they compute:

Number of levels using (3,2) = 1

Number of levels using (4;2) = 1

Equivalent delay: 1.5

Or how about for 9 operands how did they compute:

Number of levels using (3,2) = 4

Number of levels using (4;2) = 3

Equivalent Delay: 4.5

The textbook also points out that the equivalent delay of a (4;2) compressor carry save tree with 9 operands (4.5) is bigger than that of a carry save tree using (3,2) counters. Why is that?

What are the general conditions when one is bigger than the other?

The following is an image of a (4:2) compressor taken from this book.

enter image description here

The truth table provided for this compressor is:

enter image description here

where $ a=b=c=1$ and $ d=e=f=0$ . I think these constants are used to generalize the circuit.

An adder tree that uses (4;2) compressors will have a more regular struc-ture and may have a lower delay than an ordinary CSA tree made of (3,2) counters. Table 6.8 compares the delays of carry-save trees using either (3,2) counters or (4;2) compressors. Since the delay of a (4;2) compressor is 1.5 times that of a (3,2) counter, the number of levels of (4;2) compressors in column 3 is multiplied by 1.5 to yield the equivalent delay in column 4. Note that the equivalent delay of a carry save tree using (4;2) compressors (column 4) is not always smaller than that of a carry save tree using (3,2) counters (column 2). For example, for nine partial products, (3,2) counters will yield a carry save tree with an overall lower delay. Various other counters and compressors can be employed in the implementation of the addition tree for the partial product accumulation; for example, (7,3) counters

Please look at the bold face sentence above: enter image description here

Do PCs have a volumetric carry capacity limit?

In the Player Starting Guide (a summary of the PHB) it says that characters can carry an amount of Strength Value × 15 = weight limit in pounds. But later, in the gear section, there is a table about Container Capacity (usually cubic feets) of backpacks, chests, barrels, vials, etc, even about backpacks it says:

You can also strap items, such as a bedroll or a coil of rope, to the outside of a backpack.

So… are PCs limited by carry weight and by volume?

If that is true, how much initial volume can a character carry?

Is volume tracked per storage item or all as a whole (I mean, if I have an item which size 2 ft3 and two bags with 1 ft3 each one, can I carry that item or not?)?

Does casting Contingency via Wish remove the requirement to carry a statuette?

When used to cast another spell, Wish states:

You don’t need to meet any requirements in that spell, including costly Components.

(PHB 288)

Contingency states:

…contingency ends on you if its material component is ever not on your person.

(PHB 227)

Does this mean that, when cast via Wish, you are always considered to have the statuette on you?

Addition of 3 bits using Full Adder when the initial carry bit is 0

How do I add 3 bits using full adder and basic gates, when the initial carry bit is 0??

I have tried using two full adders where two terminals of the first adder gets the first two inputs then the output of this adder goes to of the inputs of the second adder and the third input is given to the second input terminal of the second adder. The carry out from the first adder goes to the carry input of the second adder.

I’ve added a picture of the circuit which was created by using Logisim(software for designing digital logic circuit).

But it doesn’t give the right answer.

normally in binary system, for addition of three bit sum is 1 and carry output bit is 1.

1+1+1 = 1 & carry bit = 1

But as you can see in the picture of the circuit I designed below, output of my circuit for adding three binary digit, sum is 0 and carry output bit is 1. which is not the right answer

1+1+1, is sum = 0 & carry = 1

The reason of this is clear to me. But I can’t design the exact circuit. How do I design the circuit that can add 3 bit when initial carry is 0?

enter image description here

Asavir prestige class grant Djinni’s Blessing (Su) : “The mount … carry a second rider without penalties”, how rule it?

Regarding the asavir prestige class :

And at the read of the Djinni’s Blessing (Su) : When an asavir reaches 4th level, her mount receives the blessing of the djinn, making it swift and tireless. The mount’s speed increases by 10 feet, it doesn’t take movement penalties from wearing barding, and it can carry a second rider without penalties. When the asavir reaches 8th level, her mount’s speed increases by an additional 10 feet.

I’m asking how rule it ? Does both are on the same Saddle ? or two distinct Saddle are need ? In the particular case of a mounted charge, the two riders and the mount declare charge (like for one rider and mount) ? in the case of ride-by-attack feat, does the two riders need it to performed it ?

Does the two rider (considering two M riders on a L mount) are considering adjacent or sharing the same space ? in the second case with or without the malus due to it ?

Thanks for your responses.

Can a blood hawk animal companion carry around their beast master? [duplicate]

This question already has an answer here:

  • Can my familiar fly with a small person? 3 answers

Let’s say a gnome Beast Master ranger chooses a Blood Hawk animal companion, can the PC be flown around (carried) by their companion?

The blood hawk has a strength of 6, and thereby a carry capacity of 90lb.

Gnomes are between 3 and 4 feet tall and average about 40 pounds. (PHB p.37)

If yes, does the PC have free hands to act as normal while carried?

Important aspects to carry out different businesses or companies simultaneously

When we talk business, companies, licenses of our websites, I think we have to take different aspects into consideration. Especially if we are creating different websites or companies. We have to widely diversify our goal, maintain the essence of our business and do each one, in a unique way, without moving away from our business model of course. If we are dealing with different potential clients in different companies, and we are starting each one, the best way is to save as much as…

Important aspects to carry out different businesses or companies simultaneously

Can I see due to the mundane light source that I carry while I’m invisible?

(I found a similar question about seeing with magical light while invisible, but I have a question about mundane light, based on a scenario that came up in today’s session.)

I’m a human (and so I don’t have darkvision), in a deep dungeon (and so there’s no light around), carrying a lantern. (I’m assuming the answer doesn’t particularly change depending on the type of nonmagical light source, but if it matters let’s call it a bullseye lantern.) I drink a potion of invisibility.

Since I’m carrying the lantern, it becomes invisible too. Can others still see the light emitted from it, though? More importantly, can I still see my surroundings based on this light, or do I become effectively blinded?