The Elements of Computing Systems: Building a Modern Computer from First Principles (14 page)
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Authors: Noam Nisan,Shimon Schocken
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4.1.2 Languages
4.2.1 Overview
A machine language program is a series of coded instructions. For example, a typical instruction in a 16-bit computer may be 1010001100011001. In order to figure out what this instruction means, we have to know the rules of the game, namely, the instruction set of the underlying hardware platform. For example, the language may be such that each instruction consists of four 4-bit fields: The left-most field codes a CPU operation, and the remaining three fields represent the operation’s operands. Thus the previous command may code the operation set R3 to R1 + R9, depending of course on the hardware specification and the machine language syntax.
Since binary codes are rather cryptic, machine languages are normally specified using both binary codes and symbolic mnemonics (a mnemonic is a symbolic label whose name hints at what it stands for—in our case hardware elements and binary operations). For example, the language designer can decide that the operation code 1010 will be represented by the mnemonic add and that the registers of the machine will be symbolically referred to using the symbols R0, R1, R2, and so forth. Using these conventions, one can specify machine language instructions either directly, as 1010001100011001, or symbolically, as, say, ADD R3,R1,R9.
Taking this symbolic abstraction one step further, we can allow ourselves not only to read symbolic notation, but to actually write programs using symbolic commands rather than binary instructions. Next, we can use a text processing program to parse the symbolic commands into their underlying fields (mnemonics and operands), translate each field into its equivalent binary representation, and assemble the resulting codes into binary machine instructions. The symbolic notation is called assembly language, or simply assembly, and the program that translates from assembly to binary is called assembler.
Since different computers vary in terms of CPU operations, number and type of registers, and assembly syntax rules, there is a Tower of Babel of machine languages, each with its own obscure syntax. Yet irrespective of this variety, all machine languages support similar sets of generic commands, which we now describe.
4.1.3 CommandsArithmetic and Logic Operations
Every computer is required to perform basic arithmetic operations like addition and subtraction as well as basic Boolean operations like bit-wise negation, bit shifting, and so forth. Here are some examples, written in typical machine language syntax:
Every computer is required to perform basic arithmetic operations like addition and subtraction as well as basic Boolean operations like bit-wise negation, bit shifting, and so forth. Here are some examples, written in typical machine language syntax:
Memory Access
Memory access commands fall into two categories. First, as we have just seen, arithmetic and logical commands are allowed to operate not only on registers, but also on selected memory locations. Second, all computers feature explicit load and store commands, designed to move data between registers and memory. These memory access commands may use several types of addressing
modes
—ways of specifying the address of the required memory word. As usual, different computers offer different possibilities and different notations, but the following three memory access modes are almost always supported:
Memory access commands fall into two categories. First, as we have just seen, arithmetic and logical commands are allowed to operate not only on registers, but also on selected memory locations. Second, all computers feature explicit load and store commands, designed to move data between registers and memory. These memory access commands may use several types of addressing
modes
—ways of specifying the address of the required memory word. As usual, different computers offer different possibilities and different notations, but the following three memory access modes are almost always supported:
■
Direct addressing
The most common way to address the memory is to express a specific address or use a symbol that refers to a specific address, as follows:
Direct addressing
The most common way to address the memory is to express a specific address or use a symbol that refers to a specific address, as follows:
■
Immediate addressing
This form of addressing is used to load constants—namely, load values that appear in the instruction code: Instead of treating the numeric field that appears in the instruction as an address, we simply load the value of the field itself into the register, as follows:
Immediate addressing
This form of addressing is used to load constants—namely, load values that appear in the instruction code: Instead of treating the numeric field that appears in the instruction as an address, we simply load the value of the field itself into the register, as follows:
■
Indirect addressing
In this addressing mode the address of the required memory location is not hard-coded into the instruction; instead, the instruction specifies a memory location that holds the required address. This addressing mode is used to handle pointers. For example, consider the high-level command x=foo[j], where foo is an array variable and x and j are integer variables. What is the machine language equivalent of this command? Well, when the array foo is declared and initialized in the high-level program, the compiler allocates a memory segment to hold the array data and makes the symbol foo refer to the base address of that segment.
Indirect addressing
In this addressing mode the address of the required memory location is not hard-coded into the instruction; instead, the instruction specifies a memory location that holds the required address. This addressing mode is used to handle pointers. For example, consider the high-level command x=foo[j], where foo is an array variable and x and j are integer variables. What is the machine language equivalent of this command? Well, when the array foo is declared and initialized in the high-level program, the compiler allocates a memory segment to hold the array data and makes the symbol foo refer to the base address of that segment.
Now, when the compiler later encounters references to array cells like foo[j], it translates them as follows. First, note that the jth array entry should be physically located in a memory location that is at a displacement j from the array’s base address (assuming, for simplicity, that each array element uses a single word). Hence the address corresponding to the expression foo[j] can be easily calculated by adding the value of j to the value of foo. Thus in the C programming language, for example, a command like x=foo[j] can be also expressed as x=*(foo+j), where the notation “*n” stands for “the value of Memory[n]”. When translated into machine language, such commands typically generate the following code (depending on the assembly language syntax):
Flow of Control
While programs normally execute in a linear fashion, one command after the other, they also include occasional branches to locations other than the next command. Branching serves several purposes including repetition (jump backward to the beginning of a loop), conditional execution (if a Boolean condition is false, jump forward to the location after the “if-then” clause), and subroutine calling (jump to the first command of some other code segment). In order to support these programming constructs, every machine language features the means to jump to selected locations in the program, both conditionally and unconditionally. In assembly languages, locations in the program can also be given symbolic names, using some syntax for specifying labels. Figure 4.1 illustrates a typical example.
While programs normally execute in a linear fashion, one command after the other, they also include occasional branches to locations other than the next command. Branching serves several purposes including repetition (jump backward to the beginning of a loop), conditional execution (if a Boolean condition is false, jump forward to the location after the “if-then” clause), and subroutine calling (jump to the first command of some other code segment). In order to support these programming constructs, every machine language features the means to jump to selected locations in the program, both conditionally and unconditionally. In assembly languages, locations in the program can also be given symbolic names, using some syntax for specifying labels. Figure 4.1 illustrates a typical example.
Figure 4.1
High- and low-level branching logic. The syntax of goto commands varies from one language to another, but the basic idea is the same.
High- and low-level branching logic. The syntax of goto commands varies from one language to another, but the basic idea is the same.
Unconditional jump commands
like JMP beginWhile specify only the address of the target location.
Conditional jump
commands like JNG R1,endWhile must also specify a Boolean condition, expressed in some way. In some languages the condition is an explicit part of the command, while in others it is a by-product of executing a previous command.
like JMP beginWhile specify only the address of the target location.
Conditional jump
commands like JNG R1,endWhile must also specify a Boolean condition, expressed in some way. In some languages the condition is an explicit part of the command, while in others it is a by-product of executing a previous command.
This ends our informal introduction to machine languages and the generic operations that they normally support. The next section gives a formal description of one specific machine language—the native code of the computer that we will build in chapter 5.
4.2 Hack Machine Language Specification4.2.1 Overview
The Hack computer is a von Neumann platform. It is a 16-bit machine, consisting of a CPU, two separate memory modules serving as instruction memory and data memory, and two memory-mapped I/O devices: a screen and a keyboard.
Memory Address Spaces
The Hack programmer is aware of two distinct address spaces: an instruction memory and a data memory. Both memories are 16-bit wide and have a 15-bit address space, meaning that the maximum addressable size of each memory is 32K 16-bit words.
The Hack programmer is aware of two distinct address spaces: an instruction memory and a data memory. Both memories are 16-bit wide and have a 15-bit address space, meaning that the maximum addressable size of each memory is 32K 16-bit words.
The CPU can only execute programs that reside in the instruction memory. The instruction memory is a read-only device, and programs are loaded into it using some exogenous means. For example, the instruction memory can be implemented in a ROM chip that is pre-burned with the required program. Loading a new program is done by replacing the entire ROM chip, similar to replacing a cartridge in a game console. In order to simulate this operation, hardware simulators of the Hack platform must provide a means to load the instruction memory from a text file containing a machine language program.
Registers
The Hack programmer is aware of two 16-bit registers called D and A. These registers can be manipulated explicitly by arithmetic and logical instructions like A=D-1 or D=!A (where “!” means a 16-bit Not operation). While D is used solely to store data values, A doubles as both a data register and an address register. That is to say, depending on the instruction context, the contents of A can be interpreted either as a data value, or as an address in the data memory, or as an address in the instruction memory, as we now explain.
The Hack programmer is aware of two 16-bit registers called D and A. These registers can be manipulated explicitly by arithmetic and logical instructions like A=D-1 or D=!A (where “!” means a 16-bit Not operation). While D is used solely to store data values, A doubles as both a data register and an address register. That is to say, depending on the instruction context, the contents of A can be interpreted either as a data value, or as an address in the data memory, or as an address in the instruction memory, as we now explain.
First, the A register can be used to facilitate direct access to the data memory (which, from now on, will be often referred to as “memory”). Since Hack instructions are 16-bit wide, and since addresses are specified using 15 bits, it is impossible to pack both an operation code and an address in one instruction. Thus, the syntax of the Hack language mandates that memory access instructions operate on an implicit memory location labeled “M”, for example, D=M+1. In order to resolve this address, the convention is that M always refers to the memory word whose address is the current value of the A register. For example, if we want to effect the operation D = Memory[516] - 1, we have to use one instruction to set the A register to 516, and a subsequent instruction to specify D=M-1.
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