Continuing the discussion through abstraction level 1-3 in the last post, we look at level 4: machine language in detail in this post.

Level 4: Machine language

Before we build the computer, let’s understand what we want the computer to be able to do from a user point of view.

The reason that computers can do a lot of different tasks is because it is modeled based on Universal Turing Machine in theory, and Von Neumann Architecture in practice.

The machine is designed to read binary instructions and perform different tasks. The binary instructions are called machine language. It is one of the most important elements of computer science because it is how software controls hardware.

Machine language consists of three conceptual parts:

  1. Operations. It has a list of operations encoded in binary to go through. Each operation instructs it to do a different thing.
  2. Program counter. Let the computer know which operation to execute next.
  3. Address. Let the computer know what to operate on, where it can get it and where to put the output.

We humans don’t program in machine language. We write high level language and let the compiler to translate it to machine language. But since now we are learning how to build a computer, we need to understand machine language.

Machine language is just a sequence of bits. For example, the ADD operation is defined as 0100010, say a variable R3 is 0011, R2 is0010, then 010001000110010 means ADD R3 R2.

We allow humans to write machine language via Assemly language. In Level 6, we will build “Assembler” to convert it into bits.

Machine language is usually in close correspondence to actual hardware architecture. If we want more powerful machine language operations, we need more advanced hardware.

Common machine operations:

  • Arithmetic
  • Logical operations
  • Flow control: goto instruction Y, if A then goto instruction C

Differences between machine languages:

  • Richness of operations (division? bulk copy?)
  • Data types (width, floating point…)

For example, some machines can only handle 8-bit arithmetic. To do a 64-bit addition, it can still do it by iterating through its 8 bits and relying on algorithm. But a 64-bit machine can do it much faster and more easily than the 8-bit machine.

Memory hierarchy

Accessing a memory location is expensive.

  • large memory has long addresses
  • getting the memory content into CPU takes time (slow compared to CPU carrying out the operation)

The solution was introduced by Von Neumann when he built the first computer: memory hierarchy.

We have CPU registers (smallest and fastest), then cache, main memory, and disk (biggest and slowest). Smaller memory is faster because there are only a few registers, the addresses are short, and they sit closer to CPU.

CPU registers

CPU registers are built with the fastest technology. And since they sit inside the CPU, there’s almost no delay.

There are 2 types of registers in the CPU.

  • Data registers. We can put numbers in them directly.
  • Pointer to main memory, e.g. put variable X into @A where A is an address in the main memory.


CPU needs some kind of protocol known as drivers to talk to input/output devices, such as mouse, keyboard, camera, sensors, screen, printer, sound, etc.

One general method of interaction uses “memory mapping”, e.g.

  • Memory location 12345 holds the direction of the last mouse movement.
  • Memory location 45678 is not a real memory location but a way to tell the printer which paper to use.

Flow control

Flow control is the way we tell the hardware which instruction to execute next.

There is unconditional jump so we can loop:

There is conditional jump if a condition is met:

The Hack computer and machine language

The Hack computer we are building is going to a 16-bit computer with an architecture shown below:

It has

  • a data memory (RAM)
  • an instruction memory (ROM)
  • a CPU consists of 16-bit ALUs that performs 16-bit instructions
  • some buses to move data between them. Think of them as highways of 16 lanes moving 16-bit data around.

Hack software

We design the Hack machine language to have 2 types of instructions:

  • 16-bit A-instructions
  • 16-bit C-instructions

Hack program = a sequence of instructions written in the Hack machine language.

The Hack program is loaded into the instruction memory (ROM), then the reset button is pushed to start the program. The reset button is pushed once for one program.

The Hack machine language recognizes 3 registers:

  • D register: holds a 16-bit value
  • A register: holds a 16-bit value or an address
  • M register: called the selected memory register, a 16-bit RAM register addressed by A.

Notice that ROM (which stores the instructions) isn’t included in the 3 registers!


Example: @100

When this A-instruction is executed, the A register holds 100, and RAM[100] is selected in the M register (RAM).

// Set RAM[100] to -1
@100    // A=100, select RAM[100]
M = -1  // RAM[100]=-1

The above Hack machine language means we select RAM[100] by setting A register to 100. M denotes the memory content of RAM[100], we assign -1 to it.


C-instruction is the work horse of the language. It has 3 fields: dest = comp ; jump

  1. Computation. Consists of logical operations on A, D and M.
  2. Destination (optional)
  3. A jump directive (optional)

Refer to the slide above for possible comp, dest, jump values.

Example: set RAM[300] to D-1

M = D-1  // D-1 is in the predefined comp as shown above

Example: if D-1 == 0, jump to execute the instruction stored in ROM[56]

@56         // A=56
D-1; JEQ    // if D-1 == 0, goto 56

JEQ checks if comp equals 0, if yes then jump to address A (keep in mind that jump aims at ROM addresses, not RAM). In this case, comp is D-1, so JEQ checks if D-1 equals 0.

Example code:

M=A-1; JEQ

What does this do?

  1. @1 sets A register to 1.
  2. Compute comp which is A-1: A-1 equals 0.
  3. Then it stores the result 0 into the M register, RAM[1], because A is 1.
  4. JEQ checks if comp equals 0. Yes.
  5. The next instruction is ROM[1] because A is 1.

We don’t need to remember all the possible values for the 3 registers. For details, check the website.

Hack language specification

We have two ways of specifying machine language code, one in symbols and one in binary numbers. An assembler can translate symbolic code into binary code.

A-instruction specification

A-instruction has an “op code” (first bit in binary code) of 0 at the beginning of the binary code.

C-instruction specification

C-instruction has an “op code” of 1, followed by 2 bits we don’t use. By convention we set them to 1.

Here is a table where we can convert symbols to binary codes.

For example, if we want to convert D+1, we find the symbol, it’s in the column a=0, and has a value of 011111.

So the comp field D+1 is 1110011111.

We also have a table for dest the destination field.

Similarly, we have a table for jump values. Altogether we have everything in one slide here:

Finally, here is an example of a small Hack program and its translation to binary.

Working with registers and memory using machine language

Some examples

// D=10
@10     // There is no directive to directly set D=10. Set A=10 first
D=A     // and set D=A

// D++
D=D+1   // This is easy

// D = RAM[17]

// RAM[17] = D

// RAM[17] = 10

// RAM[5] = RAM[3]

Here’s another example:

Note that the white spaces are ignored, and each line of code has a line number in the background automatically.

How to terminate the program properly

We haven’t talk about program termination. If we execute our code naively, a malicious hacker could add malicious code after our code to do bad things. It is called NOP slide, meaning they added null operations after the actual code and before the malicious code to hide the latter.

We use the fact that the computer never stands still and always executes something, we end the program with an infinite loop so it is under our control. This is the best practice for program termination.

0; JMP

Built-in symbols

The Hack assembly language features built-in symbols which are virtual registers, not real registers. The symbols are R0, R1, R2, ... , R15 and they correspond to values 0, 1, 2, ..., 15.

Why do we need these virtual registers?

It is purely for style and readability.

For example,

// RAM[5]=15


The two @x lines are intended to do completely different things. The first is to set A and then set D. The second is to get address 5 in RAM and store D there.

It means when we see @x we don’t know what it wants to do until we see the next line of code. So we introduce R5,

// RAM[5]=15


When we use @R5 it’s exactly the same as @5, but it means finding the address 5 so that it’s more readable for people.

Here are all the built-in symbols:

Branching, variables, iteration using machine language


In any high level language there are many branching mechanisms such as if-else, while, switch, etc. In machine language, there is only one: goto using the jump directives.


// Program: signum.asm
// Computes:
//   if R0 > 0:
//       R1 = 1
//   else:
//       R1 = 0

D=M  // D = RAM[0]

D; JGT  // if R0 > 0, goto 8

M=0  // RAM[1] = 0
0; JMP  // end of program

M=1  // R1=1

0; JMP  // end of program

You can see this code is quite unreadable if there’s no comment or documentation. One thing we introduce to make it more readable is labels. One example is shown below. (POSITIVE) is a label that points to its next line. @POSITIVE is using the label to goto that line. This way we have a much more readable branching mechanism.


Say we want to exchange the values of R0 and R1:

// Program: flip.asm
// Flips the value of RAM[0] and RAM[1]

// temp = R1
// R1 = R0
// R0 = temp

The people who created the Assembler can define a contract: @somevar with no label (somevar) means it’s a variable, and it will use RAM[program_base_address+16]. Any new variable will increment 16, i.e. use +17, +18, etc.


Suppose we want to compute 1+2+...+n, we need an accumulator variable and an iteration in a high level language. The machine code is shown below:


From the machine’s perspective, an array is just a block of memory that starts at a certain base memory location with a certain length. The following example is to set -1 into the array.

First we set 2 variables, the base memory location arr and length n. Then we set the variable i. To achieve RAM[arr+i] = -1, we set register A to be D+M. This is the first time we set A using an arithmetic operation.

Variables that store memory addresses like arr and i are called pointers. When we need to access memory using a pointer, we need an instruction like A=M.

Typical pointer semantics: “set the address register to the content of some memory register”.

Input/Output using machine language

The computer gets data from humans via input devices like the keyboard, and outputs to output devices like the display.

In high level languages such as Java and Python, we write code using input devices and the output devices give us the high level results such as text, graphics, audio and video. This is in the realm of software hierarchy and isn’t the focus now. Now we focus on the hardware hierarchy.

All the high level functionalities depend on the low level operations on bits.

Screen output

There is a part in RAM that’s called the Screen Memory Map which refreshes many times per second. It directly controls the display on the screen. When we need to display something, we manipulate this part of the memory.

The Hack computer assumes a physical screen of 256x512 pixels black and white. In the memory, we use a chunk of 16-bit registers to represent this pixel matrix.

Since one word is 16-bit, and one row in the screen is 512 pixels, we need 512/16=32 words to represent a row. Doing some math we can calculate the memory address of each pixel.

Note that the whole screen memory chunk resides inside the big RAM and it has a starting address. We use a chip Screen[] to add the starting base address to the pixel coordinates to get the actual memory address.

You might be shocked how much work we need to do just to manipulate one pixel. That’s the reality at low level!

Keyboard input

A physical keyboard is connected to the Keyboard Memory Map in RAM. The good thing is that we only need one 16-bit register to represent the keyboard.

Each key has a binary scan code that goes into the keyboard memory map. If the keyboard is not pressed, the scan code is 0.

To see what key is pressed, just probe the keyboard chip. In the Hack computer, the keyboard memory map is at RAM[24576].

Here is a complete scan code mapping for the Hack computer keyboard:

Notice that the keyboard memory map has 16 bits, it can represent $2^{16}=65536$ different keys which is more than enough even for unicode characters.

Draw a rectangle with Hack programming

Let’s consider the “hello world” program of computer graphics: drawing a rectangle.

Let’s focus on the pseudocode. The goal is to manipulate the Screen Memory Map to show the rectangle.

The following is the real Hack code

Compiler: translates high level language to machine code

This is From NAND to TETRIS part I and we don’t concern ourselves with the compiler which translates a high level language to machine code. In part II, there’s material showing how to write a compiler and an operating system.


Hack is a simplified version of the machine language. The machine language that controls our day-to-day personal computers is more complex and has more features such as floating point arithmetic. However, we can always use software to expand the capabilities of the machine language, and that is in the part II of From NAND to TETRIS.

Go to Part III


Coursera From NAND To TETRIS