Assume that registers $s0 and $s1 hold the values 0x7 and

0x95, respectively. assume these are twos complement numbers.

a. what is $s0 in decimal?

b. what are the 8 most-significant bits?



c. what is the decimal value of those 8 msbs?



d. what is $s1 in decimal?

e. what are the 8 most-significant bits?



f. what is the decimal value of those 8 msbs (remember, it’s twos complement)?



g. drop the last 6 hex digits from both numbers – they’re just trailing zeros.

if we need to subtract $s1, we’ll need to calculate its twos complement. using only the first two hex characters as input, what is the twos complement value?



h. what is the decimal value of those 8 bits?



i. calculate the value of $t0 for the following assembly code:

add $t0, $s0, $s1

but do it with just the first two hex characters, as if we had only 8-bit registers.

in decimal: (hint: it’s a number between -10 and +10)

j. what about in hex (remember, use two hex characters for 8 bits):

k. can we just add back the trailing six "0" hex characters we eliminated? to find out, calculate the result using all 8 hexadecimal values for each source operand, and use 8 for the output. what is the value of $t0 from the same command?

add $t0, $s0, $s1

in value in hex:

l. does the "trick" work? can we truncate inputs to ignore the same number of trailing zeros from both operands and still get the right answer in hex/binary?

no

m. is there a carry-out from this equation (did we produce a 33rd bit when using the full 32-bit operands, or a 9th bit when using the 8-bit operands)?

no

n. does that carry-out mean we have overflow? explain.

noexplain:

o. we now turn to subtraction. we will need to calculate the twos complement of $s2 so we can add it instead of subtract it. what is that value?

in hex (8 characters):

p. for the contents of registers $s0 and $s1 as specified above, what is the value of $t0 for the following assembly code?

sub $t0, $s0, $s1

$t0 in hex:

q. try using only the first 8 bits like we did earlier, as if the problem were:

sub $t0, 0x70, -0x95

first, what is -0x95? calculate the twos complement of 0x95?

in hex:

r. now, what is 0x70 + -0x95? substitute your 2’s comp value for -0x95 to make it positive, and then add instead of subtracting.

in hex:

s. what about in binary?

t. is there carryout in this result? yes no

u. is there overflow (invalid answer)?

yes no. explain: