[컴퓨터구조] 3. Arithmetic for Computers (1)

Example 6

main:
   li   $s0, 0x06
   li   $s1, 0x10
   move $a0, $s0       // $s0에서 $a0로 move
   move $a1, $s1
   jal  sum
   nop
   
   move $s3, $v0       // Get the result
   
   move $a0, $s3       // Print the sum
   li   $v0, 1
   syscall
   
   li   $v0, 1         // Exit
   syscall
   
   
sum:
   add  $t1m $a0, $a1
   move $v0, $t1
   jr   $ra            // Return to the main function
   nop

 

Memory Layout

Memory Layout

• Stack: automatic storage
• Dynamic data: heap
• Static data: global variable
• Text: program code

 

Jump Addressing

: j, jal

Jump targets could be anywhere in text segment.

J-type

 

Branching Far Away

: beq, bne

If branch target is too far to encode with 16-bit offset, assembler rewrite the code.

// Example

beq  $s0, $s1, L1     // cannot reach L1 (가정)

bne  $s0, $s1, L2
j    L1               // jump 연산으로 변경한다.

I-type

• Branch: 16-bit 내에서 branch 가능
• Jump: 어디든 갈 수 있음

 

Addressing Mode Summary

Addressing Mode Summary

 

 

Assembler Pseudo Instructions

• Pseudo instructions: Figments of the assembler's imagination.
• Native instructions

// move --> add

move $t0, $t1            // $t1에서 $t0로 move

add  $t0, $zero, $t1     // $t0 = 0 + $t1

blt --> slt, bne

blt  $t0, $t1, L     // if($t0 < $t1), branch to L

slt  $at, $t0, $t1   // Set Less Than, if ($t0 < $t1), $at = 1
bne  $at, $zero, L

 

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Ch3: Logic and Arithmetic

Positional Notation of Numbers

• Binary numbers (2진수)
• Hexadecimal numbers (16진수)

 

Range of Unsigned Binary Numbers

Range of Unsigned Binary Numbers

 

 

Unsigned vs. Signed Numbers

• unsigned int x;
• int x;

 

 

Signed Number Representations

1) Sign/Magnitude Representation

Sign + Magnitude

 

2) One's Complement Representation

One's Complement Representation

 

3) Biased

Biased

 

4) Two's Complement Representation

: 뒤집고, +1

Range of Two's Complement Numbers

 

 

Sign Extension

: Copy the sign bit.

Sign Extension Example

 

Zero-Padding for Unsigned Numbers

: Copy "zeros".

Zero Padding Example

 

Sign Extension in MIPS

• Load-byte (lb) instruction: Loads an 8-bit signed number from memory to register.
• Load-byte unsigned (lbu) instruction: Loads an 8-bit unsigned number from memory to register.

 

Sign Extension in MIPS I-Format Instructions

I-Format instruction

• I-Format instruction --> 16-bit immediate field
• MIPS operations: defined on 32-bit registers. (MIPS 아키텍처에서 사용하는 레지스터는 32-bit 크기이다.)

--> Sign extension performed on immediate operands.

 

 

Signed & Unsigned Comparisons

• slt (Set Less Than): signed comparison
• sltu (Set Less Than Unsigned): unsigned comparison

Example

--> 어떤 instruction을 쓰느냐에 따라 답이 달라질 수 있다.

 

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Binary Addition

Binary Addition

 

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SBY 5-2

1. Write down an MIPS assembly code that gets two integers from a user console, and sums those values in a subroutine.

main:
   li   $v0, 5
   syscall
   move $s0, $v0     # the first read integer at $s0
   li   $v0, 5
   syscall
   move $s1, $v0     # the second read integer at $s1
   
   move $a0, $s0     
   move $a1, $s1
   jal  sum_it
   nop
  
# Get the result
   move $s3, $v0          
   
# Exit the program
   li   $v0, 10
   syscall
   
   
sum_it:
   add  $t0, $a0, $a1
   move $v0, $t0
   jr   $ra
   nop

 

2. Can you draw the memory layout and specify what kind of data is stored at which area?

Memory Layout

• Stack: automatic storage
• Dynamic data: heap
• Static data: global variable
• Text: program code

 

3. What are the main differences between branch addressing and jump addressing?

• Branch: I-format (constant address is 16-bit) --> 16-bit 내에서 branch할 수 있다.
  --> PC-relative addressing: target address = PC + offset*4
• Jump: J-format (address is 26-bit) --> 멀리까지 jump할 수 있다.
  --> Direct jump addressing

I-format vs. J-format

 

4. Represent -21 using 8-bit with 1) sign/magnitude, 2) one's complement, 3) two's complement.

1. 10010101
2. 11101010
3. 11101011