Observe the following binary addition:

3 2 1 0 ? 0 ? x + ? ? ? y -------- ? ? ? q +? 1 ? ? k -------- ? ? 1 s o=? l=1

Be careful not to miss the overflow flag o and the less-than flag l. Overflow (o) is defined differently for addition. It is defined as

o=MSb(x)MSb(y)!MSb(s) + !MSb(x)!MSb(y)MSb(s)

where MSb means the most significant bit of. The less-than l flag is still defined as

l=o xor MSb(s)

The first part is to figure out all the unknown bits marked as question marks (?). The sequence of figuring out the unknown bits must be self contained in this answer and not reliant on the answer of another question. For each bit, clearly state which bit, its value, and how you use the definitions to derive it. As an example (probably wrong):

• k2 = 1 because k[i]=x[i] xor q[i], and at this point x2=1 and q2=0

You may update the unknown bits of the addition in-place, but the explanation must be sequential. If the order does not make sense, points will not be earned.

Note that the unknown bit can be from x, y, q, k, s, as well as also the overflow (o) and less (l) bits/flags. t0 should not be assumed 0 as it is an input pin.

Use this area to explain how you get th unknown bits resolved, a bullet list makes the answer easier to read:

The second part is to figure out the values represented. Use the following bullets to enter your answer. Include calculations that show how you get the values. Quoting from the number wheel is not an acceptable explanation.

• the unsigned interpretation of x:

• the signed interpretation of x:

• the unsigned interpretation of y:

• the signed interpretation of y:

• the unsigned interpretation of s:

• the signed interpretation of s:

The third part is to show how to compute k3 using the following steps;

• what is the multibit p term? For example p = 110 means p0=0, p1=1 and p2=1

• your answer: p =

• what is the multibit g term? (Similar format as p)

• your answer: g =

• spell out the carry lookahead expression of k3, and substitute each p or g bit with the actual value

• your answer: k3 =

Question 2 of 8

Observe the following binary addition:

3 2 1 0 ? ? ? x + ? 0 ? y -------- ? ? ? q +0 ? ? 0 k -------- ? ? ? s o=1 l=?

Be careful not to miss the overflow flag o and the less-than flag l. Overflow (o) is defined differently for addition. It is defined as

o=MSb(x)MSb(y)!MSb(s) + !MSb(x)!MSb(y)MSb(s)

where MSb means the most significant bit of. The less-than l flag is still defined as

l=o xor MSb(s)

The first part is to figure out all the unknown bits marked as question marks (?). The sequence of figuring out the unknown bits must be self contained in this answer and not reliant on the answer of another question. For each bit, clearly state which bit, its value, and how you use the definitions to derive it. As an example (probably wrong):

• k2 = 1 because k[i]=x[i] xor q[i], and at this point x2=1 and q2=0

You may update the unknown bits of the addition in-place, but the explanation must be sequential. If the order does not make sense, points will not be earned.

Note that the unknown bit can be from x, y, q, k, s, as well as also the overflow (o) and less (l) bits/flags. t0 should not be assumed 0 as it is an input pin.

Use this area to explain how you get th unknown bits resolved, a bullet list makes the answer easier to read:

The second part is to figure out the values represented. Use the following bullets to enter your answer. Include calculations that show how you get the values. Quoting from the number wheel is not an acceptable explanation.

• the unsigned interpretation of x:

• the signed interpretation of x:

• the unsigned interpretation of y:

• the signed interpretation of y:

• the unsigned interpretation of s:

• the signed interpretation of s:

The third part is to show how to compute k3 using the following steps;

• what is the multibit p term? For example p = 110 means p0=0, p1=1 and p2=1

• your answer: p =

• what is the multibit g term? (Similar format as p)

• your answer: g =

• spell out the carry lookahead expression of k3, and substitute each p or g bit with the actual value

• your answer: k3 =