1. How to represent signed integers
4. Biased (excess)
B = 3 p x
000 -3
001 -2
010 -1
011
100 1
101 2
110 3
111 4
B = 127 p x
-127
128
-126
127 9
A bias value, B, is usually chosen to be roughly in the middle of the range. The actual value x of a bit pattern p is x = p - B. Given x, the bit pattern should be p = x + B.

2. CSCI206 - Computer Organization & Programming
Logical Operations, Making Decisions
zyBook: 5.6, 5.7

3. MIPS Integer Operations
Bit-wise!

4. Bitwise/logical Instructions
Category
Instruction
C operator
MIPS Instruction
Logical
shift left
<<
sll
shift right
>>
srl
bitwise AND
&
and, andi
bitwise OR |
or, ori
bitwise XOR ^
xor, xori

5. Shift Left - Machine Code
r-type instruction with an immediate!
sll $s1, $s0, 8
shift left 16 17 8
opcode rs rt rd
shift amount
function
unused (0)
0x00108A00
R[rd] = R[rt] << shamt

6. Comparison and Decision Instructions
slt rd, rs, rt ;set less than: R[rd] = (R[rs] < R[rt]) ? 1 : 0
slti rt, rs, imm ;set less than immediate
;R[rt] = (R[rs] < imm) ? 1 : 0
beq r1, r2, label ; branch to label if r1 == r2
bne r1, r2, label ; branch to label if r1 != r2

7. Common Programming Patterns in C
Decisions
if (boolean condition){
(consequent)
}else{
(alternative) }
switch (var){
case 0: //case_0_code;
break;
case 1: //case_1_code;
case 2: //case_2_code;
default: //default_code;
Loops
do{
// Code for the loop's body
// goes here.
}while(condition)
while(condition) { }
for(initialization; condition; update){
// Code for the for loop's body

8. IF lw $t1, 0($s0) ;load a from mem // assume a is an int
if (a == 1) {
// consequent code
}else{
// alternative code }
lw $t1, 0($s0) ;load a from mem
addi $t2, $zero, 1 ;set $t2 to 1
IF: beq $t1, $t2, A
; alternative code
j ENDIF
A: ; consequent code
ENDIF:
lw $t1, 0($s0) ;load a from mem
addi $t2, $zero, 1 ;set $t2 to 1
IF: bnq $t1, $t2, B
; consequent code
j ENDIF
B: ; alternative code
ENDIF:

9. If activity
if ($a0 > 127){
$v0 = 1;
} else {
$v1 = 1; }

10. if ($a0 > 127){
$v0 = 1;
} else {
$v0 = 0; }
If solution

11. DO/WHILE addi $t0, $zero, 15 x = 15; do_begin: do{ ; Loop body
// Code for the loop’s body
// goes here.
x = x - 1
} while(x >= 10)
addi $t0, $zero, 15
do_begin:
; Loop body
addi $t0, $t0, -1
slti $t1, $t0, 10
beq $t1, $zero, do_begin
do_end:

12. WHILE/DO addi $t0, $zero, 15 while_begin: x = 15 slti $t1, $t0, 10
beq $t1, $zero, while_end
; LOOP BODY
addi $t0, $t0, -1
j while_begin
while_end:
x = 15
while(x >= 10){
// Code for the loop’s body
// goes here.
x = x - 1 }

13. While activity $v0 = 0; while ($a0 > 0){ $v0 ^= 1;
$a0 = $a0 & ($a0 - 1); }

14. While solution $v0 = 0; while ($a0 > 0){ $v0 ^= 1;
$a0 = $a0 & ($a0 - 1); }
While solution

15. FOR for(i = 0; i < 10; i ++){ addi $t0, $zero, 0
// Code for the for loop's body
// goes here. }
addi $t0, $zero, 0
for_begin:
slti $t1, $t0, 10
beq $t1, $zero, for_end
; LOOP BODY
addi $t0, $t0, -1
j for_begin
for_end:

16. For activity $v0 = 0; for ( $t0 = 0; $t0 < 32; $t0++ ){
if ( ($a0 >> $t0) & 0x1 == 0x1 ){
$v0 ^= 1; }

17. For solution

18. SWITCH switch (var){ case 0: //case_0_code; break;
default: //default_code; }
BEQ var, 0, CASE_0
BEQ var, 1, CASE_1
BEQ var, 2, CASE_2
default:
; default_code
j END
CASE_0:
; case_0_code
CASE_1:
; case_1_code
CASE_2:
; case_2_code
END:

19. SWITCH (jump table) .data TABLE: .word CASE_0 .word CASE_1
.text
sll $t1, var, 2
lw $t0, TABLE($t1)
jr $t0
CASE_0:
; case_0_code
j END
CASE_1:
; case_1_code
CASE_2:
; case_2_code
END:
switch (var){
case 0: //case_0_code;
break;
case 1: //case_1_code;
case 2: //case_2_code; }
Warning: this assumes all cases are used (starting with zero) and the input is valid!

20. Pseudo branch instructions
The assembler uses the $at register and slt to implement
blt (branch less than)
bgt (branch greater than)
ble (branch less than or equal)
bge (branch greater than or equal)

21. Pseudo Branch Example blt $t0, $t1, label slt $at, $t0, $t1
pseudo-instruction
if $t0 < $t1
j label
blt $t0, $t1, label
if $t0 < $t1
$at = 1;
else
$at = 0;
if $at != 0
j label
slt $at, $t0, $t1
bne $at, $zero, label
true-instruction