Chapter 02 instructions language of the computer

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COMPUTER ARCHITECTURE

CHAPTER 2
INSTRUCTIONS:
LANGUAGE OF THE COMPUTER

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Instructions: Language of the Computer

1.

Introduction

2.

Operations of the Computer Hardware

3.

Operands of the Computer Hardware

4.

Signed and Unsigned number

5.

Representing Instructions in the Computer

6.

Logical Operations

7.

Instructions for Making Decisions

8.

Supporting Procedures in Computer Hardware

9.

Communicating with People

10. MIPS Addressing for 32-Bit Immediates and Addresses
11. Translating and Starting a Program
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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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Introduction

 To command a computer‟s hardware, you must speak its language. The
words of a computer's language are called instructions, and its vocabulary is
called an instruction set
instruction set: The vocabulary of commands understood by a given architecture

With instruction set, once you learn one, it is easy to pick up others.
This similarity occurs because all computers are constructed from hardware
technologies based on similar underlying principles and because there are a few
basic operations that all computers must provide

 The chosen instruction set in this chapter is MIPS, which is an elegant
example of the instruction sets designed since the 1980s.
Two other popular instruction sets:
• ARM is quite similar to MIPS, and more than three billion ARM processors
were shipped in embedded devices in 2008
• The Intel x86, is inside almost all of the 330 million PCs made in 2008
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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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Operations:
Example:

add a, b, c  instructs a computer to add the two variables b and c and
to put their sum in a.

operations

operands

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Fig.1 MIPS assembly language

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Example 1.

Example 2.
C/Java

f = (g + h) – (i + j);

a = b + c;
d = a – e;
MIPS

add a, b, c
sub d, a, e

C/Java

add t0, g, h
add t1, i, j
sub f, t0, t1

MIPS

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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Operands of the computer hardware
1. Register Operands
2. Memory Operands
3. Constant or Immediate Operands

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Register Operands:
 Unlike programs in high-level languages, the operands of arithmetic instructions are
restricted; they must be from a limited number of special locations built directly in
hardware called registers.
 The size of a register in the MIPS architecture is 32 bits; groups of 32 bits occur so
frequently that they are given the name word in the MIPS architecture.
(note: a word in other instruction sets is able to not be 32 bits)

 One major difference between the variables of a programming language and
registers is the limited number of registers, typically 32 on current computers.
MIPS has 32 registers.

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Memory Operands (1):
 The processor can keep only a small amount of data in registers, but computer
memory contains millions of data elements.

 With MIPS instructions, arithmetic operations occur only on registers; thus, MIPS
must include instructions that transfer data between memory and registers. Such
instructions are called data transfer instructions.

Data transfer instruction: A command that moves data between memory and
registers

 To access a word in memory, the instruction must supply the memory address
Address: A value used to delineate the location of a specific data element within a
memory array.
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 Memory is just a large, single-dimensional array, with the address acting as the
index to that array, starting at 0. For example, in Figure 2.2, the address of the third
data element is 2, and the value of Memory[2] is 10.

Fig.2 Memory addresses and contents
of memory at those locations.
This is a simplification of the MIPS
addressing; Fig.3 shows the actual
MIPS addressing for sequential word
addresses in memory.

Fig.3 Actual MIPS memory addresses and contents
of memory for those words.
The changed addresses are highlighted to contrast
with Fig.2. Since MIPS addresses each byte, word
addresses are multiples of four: there are four bytes
in a word.

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 The data transfer instruction that copies data from memory to a register is
traditionally called load. The format of the load instruction:

lw $s1,20($s2)
offset

Base address in a base register

• $s1: register to be loaded
• A constant (20) and register ($s2) used to access memory. The sum of
the constant and the contents of the second register forms the memory
address.

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Example for load.
Let‟s assume that A is an array of 100 words and that the compiler has associated the
variables g and h with the registers $s1 and $s2 as before. Let's also assume that the
starting address, or base address of the array is in $s3. Compile this C assignment
statement:

g = h + A[8];
 Compile:
lw $t0,8($s3)

Actually in MIPS, a
word is 4 bytes
lw $ t0, 32($s3)

# Temporary reg $t0 gets A[8]

add $s1,$s2,$t0 # g = h + A[8]

 The constant in a data transfer instruction (8) is called the offset, and the register
added to form the address ($s3) is called the base register
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 Alignment restriction

- In MIPS, words must start at addresses that are multiples of 4. This requirement is
called an alignment restriction, and many architectures have it. (why alignment leads
to faster data transfers – read more in Chapter 5 suggests )

- Computers divide into those that use the address of the leftmost or “big end” byte
as the word address versus those that use the rightmost or “little end” byte. MIPS is in
the Big Endian camp.

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 The instruction complementary to load is traditionally called store; it copies data
from a register to memory. The format of a store is

sw $s1,20($s2)
offset

Base address in a base register

• $s1: register to be stored
• A constant (20) and register ($s2) used to access memory. The
sum of the constant and the contents of the second register forms
the memory address.

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Example for store.
Assume variable his associated with register $s2and the base address of the array A is
in $s3. What is the MIPS assembly code for the C assignment statement below?

A[12] = h + A[8];

Compile:
lw $t0,32($s3)


add $t0,$s2,$t0

# Temporary reg $t0 gets h + A[8]

sw $t0,48($s3)

# Stores h + A[8] back into A[12]

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Constant or Immediate Operands
Many times a program will use a constant in an operation
Example:
addi $s3, $s3, 4
# $s3 = $s3 + 4

Constant or immediate operands

Notes:
 Although the MIPS registers considered here are 32 bits wide, there is a 64-bit version of
the MIPS instruction set with 32 64-bit registers. To keep them straight, they are officially
called MIPS-32 and MIPS-64.
(In this chapter, a subset of MIPS-32 is used; see more MIPS-64 in Appendix E)

 Since MIPS supports negative constants, there is no need for subtract immediate in MIPS
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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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 Humans are taught to think in base 10, but numbers may be represented in any base.
For example, 123 base 10 = 1111011 base 2.
 Numbers are kept in computer hardware as a series of high and low electronic
signals, and so they are considered base 2 numbers.
Example: the drawing below shows the numbering of bits within a MIPS word and the
placement of the number 1011:

 The MIPS word is 32 bits long, so the numbers from 0 to 232-1 (4.294.967.295)
 The least significant bit: the rightmost bit in a MIPS word (bit 0)
The most significant bit: the leftmost bit in a MIPS word (bit 31)

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Positive and negative number in computer:
Using two’s complement representation
Leading „0‟ mean positive, leading „1‟ mean negative.

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The positive half of the numbers, from 0 to 2,147,483,647ten (231 – 1), use the same
representation as before.
1000…0000two = -2,147,483,648ten
1000…0001two = -2,147,483,647ten
1111…1111two = -1ten
The 32nd bit is called the sign bit. We can represent positive and negative 32-bit
numbers in terms of the bit value times a power of 2
Two‟s complement does have one negative number -2,147,483,648ten, that has
no corresponding positive number.
Every computer today uses two‟s complement binary representations for signed
number

Note: The sign bit is multiplied by -231, and the rest of the bits are then multiplied
by positive versions of their respective base values.

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Example

Answer

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Sign Extension:
How to convert a binary number represented in n bits to a number represented with
more than n bits?

Example:
Convert 16-bit binary versions of 2ten and -2ten to 32-bit binary numbers.

2ten:
-2ten:

Taking the sign bit and replicating it to fill the new bits of larger quantity. The old
bits are simply copied into the right portion of the new word.

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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 How is an instruction (add $t0, $s1, $s2) kept in the computer?
Computer only can work with low and high electronic signals, thus an instruction
kept in computer must be represented as a serial of “0” and “1”, called machine
code/machine instruction.

 Machine language: Binary representation used for communication within a
computer system.

 In order to convert from a instruction to machine code, using instruction
format
Instruction format: A form of representation of an instruction composed of
fields of binary numbers.

Fig.4 An example of instruction format
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 Example: Translating a MIPS Assembly Instruction into a Machine Instruction
add $t0,$s1,$s2
With instruction format:

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 Answer: Translating a MIPS Assembly Instruction into a Machine Instruction
add $t0,$s1,$s2
With instruction format:

 In MIPS assembly language, registers $s0 to $s7 map onto registers 16 to 23, and
registers $t0 to $t7 map onto registers 8 to 15
 Each of these segments of an instruction format is called a field.
 The first and last fields (containing 0 and 32 in this case) in combination tell the
MIPS computer that this instruction performs addition.
 The second field gives the number of the register that is the first source operand of
the addition operation (17 = $s1)
 The third field gives the other source operand for the addition (18 = $s2).
 The fourth field contains the number of the register that is to receive the sum (8 =
$t0).
 The fifth field is unused in this instruction, so it is set to 0.

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Different kinds of instruction formats for different kinds of MIPS instructions:
 R-type(for register) or R-format

 I-type (for immediate) or I-format and is used by the immediate and
data transfer instructions

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MIPS Fields of R-format:
MIPS fields are given names to make them easier to discuss:

 op: Basic operation of the instruction, traditionally called the opcode.
Opcode: The field that denotes the operation and format of an instruction
 rs: The first register source operand.
 rt: The second register source operand.
 rd: The register destination operand. It gets the result of the operation.
 shamt: Shift amount. (the next part explains shift instructions and this term; it will
not be used until then, and hence the field contains zero.)
 funct: Function. This field selects the specific variant of the operation in the op
field and is sometimes called the function code.

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MIPS Fields of I-format:
MIPS fields are given names to make them easier to discuss:

The 16-bit address means a load word instruction can load any word within a region
of ± 215 or 32,768 bytes (±213 or 8192 words) of the address in the base register rs.
Similarly, add immediate is limited to constants no larger than ± 215

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Fig.6 shows the numbers used in each field for some MIPS instructions

Fig.6 MIPS instruction encoding.

 “reg” means a register number between 0 and 31
 “address” means a 16-bit address
 “n.a.” (not applicable) means this field does not appear in this format.
 Note that “add” and “sub” instructions have the same value in the “op” field;
the hardware uses the “funct” field to decide the variant of the operation: “add”
(32) or “subtract” (34).
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 Example: Translating MIPS Assembly Language into Machine Language
If $t1 has the base of the array A and $s2 corresponds to h, the assignment statement:
A[300] = h + A[300];
is compiled into:
lw $t0,1200($t1)
add $t0,$s2,$t0
# Temporary reg $t0 gets h + A[300]
sw $t0,1200($t1) # Stores h + A[300] back into A[300]
What is the MIPS machine language code for these three instructions?

 Answer:

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In conclusion,
1.

Instructions are represented as numbers.

2.

Programs are stored in memory to be read or written, just like numbers.
(Commercial software are often shipped as files of binary numbers)
 Treating instructions in the same way as data greatly simplifies both the
memory hardware and the software of computer systems.
 In order to perform a program, simply loading the program and data into
memory and then telling the computer to begin executing at a given
location in memory.

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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Logical Operations

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Fig.7 C and Java logical operators and their corresponding MIPS instructions.

 Shifts: moving all the bits in a word to the left or right, filling the emptied bits
with 0s (Shifting left by i bits gives the same result as multiplying by 2i)

 AND is a bit-by-bit operation that leaves a 1 in the result only if both bits of the
operands are 1
 OR is a bit-by-bit operation that places a 1 in the result if either operand bit is a 1
 NOT takes one operand and places a 1 in the result if one operand bit is a 0, and
vice versa.
 NOR: NOT OR
 Constants are useful in AND and OR logical operations as well as in arithmetic
operations, so MIPS also provides the instructions and immediate (andi) and or
immediate (ori)

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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 What distinguishes a computer from a simple calculator is its ability to make
decisions.
 In programming languages, decision making is commonly represented using the
“if” statement, sometimes combined with “go to” statements and labels.
 MIPS assembly language includes two decision-making instructions, similar to
an “if” statement with a “go to”.

Example:

beq register1, register2, L1

This instruction means go to the statement labeled L1 if the value in register1 equals
the value in register2. The mnemonic beq stands for “branch if equal”
 These such instructions are traditionally called conditional branches
Conditional branch: An instruction that requires the comparison of two values and
that allows for a subsequent transfer of control to a new address in the program based
on the outcome of the comparison.

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Conditional branch instructions of MIPS:

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 Compiling if-then-else into Conditional Branches:
In the following code segment, f, g, h, i, and j are variables. If the five variables
f through j correspond to the five registers $s0 through $s4, what is the compiled
MIPS code for this C if statement?

if (i == j) f = g + h; else f = g – h;

 Answer:
bne $s3,$s4,Else

# go to Else if i != j

add $s0, $s1, $s2

# f = g + h (skipped if i != j)

j exit

# go to Exit

else: sub $s0, $s1, $s2

# f = g – h (skipped if i = j)

exit:
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 Compiling a while loop in C
Here is a traditional loop in C:
while (save[i] == k)

i += 1;
Assume that i and k correspond to registers $s3 and $s5 and the base of the array
save is in $s6. What is the MIPS assembly code corresponding to this C segment?

 Answer:
Loop: sll $t1,$s3,2 # Temp reg $t1 = 4 * i
add $t1,$t1,$s6

# $t1 = address of save[i]

lw $t0,0($t1)

# Temp reg $t0 = save[i]

bne $t0,$s5, Exit

# go to Exit if save[i] != k

add $s3,$s3,1

#i=i+1

j Loop

# go to Loop

Exit:
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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


44

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 A procedure or function is one tool programmers use to structure programs, both to
make them easier to understand and to allow code to be reused.
 Procedures allow the programmer to concentrate on just one portion of the take at a
time.
 To execute of a procedure, the program must follow these six steps:
1. Put parameters in a place where the procedure can access them.
2. Transfer control to the procedure.
3. Acquire the storage resources needed for the procedure.
4. Perform the desired task.
5. Put the result value in a place where the calling program can access it.
6. Return control to the point of origin, since a procedure can be called from
several points in a program.

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 Registers are the fastest place to hold data in a computer, so we want to use them as
much as possible.
 MIPS software follows the following convention for procedure calling in allocating
its 32 registers:
■ $a0-$a3: four argument registers in which to pass parameters

■ $v0-$v1: two value registers in which to return values
■ $ra: one return address register to return to the point of origin

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 MIPS assembly language includes an instruction just for the procedures: it
jumps to an address and simultaneously saves the address of the following
instruction in register $ra. The jump-and-link instruction(jal) is simply written:

jal ProcedureAddress

 Nowadays, computers like MIPS use jump register instruction (jr), meaning an
unconditional jump to the address specified in a register:

jr $ra

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Terms and definitions:
 return address: A link to the calling site that allows a procedure to return to the
proper address; in MIPS it is stored in register $ra.
 caller: The program that instigates a procedure and provides the necessary parameter
values.
 callee: A procedure that executes a series of stored instructions based on parameters
provided by the caller and then returns control to the caller.
 program counter (PC): The register containing the address of the instruction in the
program being executed.
 stack: A data structure for spilling registers organized as a last-in first-out queue (In
case compiler needs more registers for a procedure than the four argument and two return
value registers).
 stack pointer (SP): A value denoting the most recently allocated address in a stack
that shows where registers should be spilled or where old register values can be found. In
MIPS, it is register $sp.
 push: Add element to stack.
 pop: Remove element from stack.
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Nested procedure:
 Procedures that do not call others are called leaf procedures.
Otherwise is called Nested procedure.
 We need to be careful when using registers in procedures, more care
must also be taken when invoking nested procedures.

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Allocating Space for New Data on the Stack
 procedure frame (activation record): The segment of the stack containing a
procedure‟s saved registers and local variables.

 frame pointer: A value denoting the location of the saved registers and local
variables for a given procedure.

Fig.8 Illustration of stack allocation (a) before, (b) during, (c) after the
procedure call.

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Allocating Space for New Data on the Heap
 Heap: It is traditionally the segment for such data structures and one is placed next
in memory.

 Text segment: The segment of a UNIX object file that contains the machine
language code for routines in the source file.

Fig.9 The MIPS memory allocation for program and data.

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Fig.10 MIPS register conventions. Register 1, called $at, is reserved for the assembler, and
registers 26-27, called $k0-$k1, are reserved for the operating system.

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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Most computers today offer 8-bit bytes to represent characters, with the American
Standard Code for Information Interchange (ASCII) being the representation that
nearly everyone follows.

Fig.11 ASCII representation of characters.
Note: upper- and lowercase letters differ by exactly 32; Values not shown include formatting
characters (8 represents a backspace, 9 represents a tab character). Another useful value is 0 for
null, the value the programming language C uses to mark the end of a string.

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


55

MIPS Addressing for 32-bit Immediates and Addresses
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Although keeping all MIPS instructions 32 bits long simplifies the hardware, there
are times where it would be convenient to have a 32-bit constant or 32-bit address.
32-Bit Immediate Operands

Example

Answer

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Example: The effect of the lui instruction

Note: The instruction lui transfers the 16-bit immediate constant field value into the
leftmost 16 bits of the register, filling the lower 16 bits with 0s.

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MIPS Addressing Mode Summary
Multiple forms of addressing are generically called addressing modes. Addressing mode
is one of several addressing regimes delimited by their varied use of operands and/or
addresses.

1. Immediate addressing, where the operand is a constant within the instruction itself

2. Register addressing, where the operand is a register

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3. Base or displacement addressing, where the operand is at the memory location
whose address is the sum of a register and a constant in the instruction

4. PC-relative addressing, where the branch address is the sum of the PC and a constant
in the instruction

5. Pseudo direct addressing, where the jump address is the 26 bits of the instruction
concatenated with the upper bits of the PC

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Decoding Machine Language
Sometimes you are forced to reverse-engineer machine language to create the original
assembly language. One example is when looking at “core dump.”

Example

Answer: (look the MIPS instruction encoding and format table)

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1.

Introduction

2.


3.


4.


5.


6.

Logical Operations

7.


8.


9.


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Translating and Starting a Program

This section describes the four steps in transforming a C program in a file
on disk into a program running on a computer.

Fig.12 A translation hierarchy for C

62

Chapter 02 instructions language of the computer

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