CSE378
Autumn 1998
Midterm Solutions
QUESTION 1:
Pseudoinstructions are instructions that are not supported by hardware.
The assembler converts them to one or more instructions which are in the
instruction set.
Examples: la, move, mul, etc.
QUESTION 2:
A:
F A B 4
1111 1010 1011 0100
- 0000 0101 0100 1100
- (2^10 + 2^8 + 2^6 + 2^3 + 2^2)
-1356
B:
1011.1011 -> 1.0111011 * 2^3 -> 0 | 130 | 0111011 ->
0 | 1000 0010 | 0111 0110 0000 0000 0000 000
0.1110010 -> 1.111001 * 2^-1 -> 0 | 126 | 111001 ->
0 | 0111 1110 | 1110 0100 0000 0000 0000 000
1.0111011 * 2^3 -> 1.0111011 * 2^3
+ 1.11001 * 2^-1 -> + 0.000111001 * 2^3
---------------- ----------------
1.100100101 * 2^3
1.10010011 * 2^3 -> 0 | 130 | 10010011 ->
0 | 1000 0010 | 1001 0010 1000 0000 0000 000
C:
-2^9 -> 2^9-1
QUESTION 3:
6.02*10^23 -> ~8*10^23
10^3 ~= 2^10
=> 10^21 ~= 2^70
8*10~23 ~= 2^80
-> 80 bits
80 < 127 -> fits in sp fp
QUESTION 4:
Not including Cin:
A B C R Cout
---------------------
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
Including Cin:
Cin A B C R Cout1 Cout2
--------------------------------
0 0 0 0 0 0 0
0 0 0 1 1 0 0
0 0 1 0 1 0 0
0 0 1 1 0 1 0
0 1 0 0 1 0 0
0 1 0 1 0 1 0
0 1 1 0 0 1 0
0 1 1 1 1 1 0
1 0 0 0 1 0 0
1 0 0 1 0 1 0
1 0 1 0 0 1 0
1 0 1 1 1 1 0
1 1 0 0 0 1 0
1 1 0 1 1 1 0
1 1 1 0 1 1 0
1 1 1 1 0 0 1
QUESTION 5:
instruction result in $s0 (x=doesnt matter)
-----------------------------------------------
xxxxxxxxxxxxxxxxxxx
lui: xxxxxxxxxxxxxxxxxxx
addiu: xxxxxxxxxxxxxxxxxxx
sll: xxxxxxxxxxxxxxx0000
not: xxxxxxxxxxxxxxx1111
andi: 0000000000000000100
$s0 = 4
QUESTION 6:
A:
0011 1100 0000 0001 0000 0000 0010 0000 ->
2^29 + 2^28 + 2^27 + 2^26 + 2^16 + 2^5
B:
0011 1100 0000 0001 0000 0000 0010 0000 ->
001111 | 00000 | 00001 | 0000 0000 0010 0000 ->
15 | 0 | 1 | 32 ->
lui $1, 32
C:
0011 1100 0000 0001 0000 0000 0010 0000 ->
0 | 0111 1000 | 0000 0010 0000 0000 0100 000
=> + 2^(120-127) * 1.0000 0010 0000 0000 01
=> (1 + 2^-7 + 2^-18) * 2^-7 = 2^-7 + 2^-14 + 2^-25
QUESTION 7:
sub $s1, $0, $s0
addi $s1, $s1, -1
QUESTION 8:
la $t0, label
label: addi $t0, $t0, -4
OR
jal label
label: move $t0, $ra
QUESTION 9:
# initialize counter, and endval
li $s2, 0
li $s4, 16
# move multiplicand to LHS
sll $s0, $s0, 16
loop:
# increment counter
addi $s2, $s2, 1
# mask out LSB of $s1 and put result in $s3
andi $s3, $s1, 1
# add $s0 to $s1 if $s3 = 1
beqz $s3, shift
add $s1, $s1, $s0
# shift the product register
shift: srl $s1, $s1, 1
# repeat
bne $s2, $s4, loop
QUESTION 10:
PC-relative addressing addes the "address field" of the instruction (which
is a signed 2s complement number) to the PC (usually PC+4) to get the address
of the next instruction, which is a word address.
QUESTION 11:
PART A:
PART B:
op | result
--------------
00 | sra A
01 | A and B
10 | A or B
11 | A or not B