stallinga.org Youtube: Computer Architecture

Lectures: Computer Architecture
on Youtube

Latest version of the book in PDF form available for free here:

Computer Architecture with (MIPS) Assembly

(my excuses to the readers of earlier versions, paper or pdf, still full of errors)

1: Digital Systems
2: Computer Architecture
3: MIPS Assembly

Computer Architecture. Digital systems:

Preview	Title	Description
	Existence of numbers	Numbers do not exist in the computer. We make a mental mapping between the physics of the computer (voltage levels, etc.) and the mathematics in our head.
	Number Systems. Ways to represent numbers	Why the decimal system (base 10) is nothing special. Base-6 is better, but the numbers get large. Base-20 is often used (Mayans) as well as Babylonian (base-60). Romans were strange. Binary is great for computing because the underlying electronics are binary.
	Number Conversions	How to convert numbers from any number base to any other number base.
	Negative Numbers	How are negative numbers stored in the computer? We will look here at three conventions: Sign-magnitude, 1s-complement and 2's-complement. We will see that 2's-complement is good because subtractions can then be done by adding the negative numbers.
	Boolean Algebra	The underlying mathematics of a computer. Boolean Algebra, that itself is based on Set Theory. The Huntington Postulates are presented that will form our basis. Some important relations are given.
	de Morgan's Laws	The de Morgan's Law tell us that the negation of a 'sum' (OR) is the 'product' (AND) of negations, NOS=PON and the negation of a 'product' (AND) is the 'sum' (OR) of negations, NOP=SON. These rules will come in very handy in the future when we design digital circuits.
	Truth Tables	Truth Tables are a way to summarize the behavior of a logic circuit. They specify the output value (0 or 1) for all combinations of input values at the gate. In total there are 2^4 = 32 possible two-input-one-output gates. The most basic ones are: AND, OR, NAND, NOR, NOT and XOR.
	Sum of Products Product of Sums	How to implement any logic function with only AND, OR and NOT operations.
	Karnaugh Maps	Karnaugh Maps are an easy way to simplify the expressions found by the SOP (sum of products) and POS (product of sums) methods
	Karnaugh Maps 2	An additional look at Karnaugh Maps. How does the XOR operation look in a KM. And how do we deal with 'don't cares'?
	Electronics, CMOS	How are the basic gates implemented in electronics? We take a look at the NOT, NAND, NOR, AND, OR and XOR gates implemented in CMOS (complementary metal oxide semiconductor) technology.
	Multiplexer	A real life example how to build a useful digital electronic circuit on basis of a functional description. A multiplexer (one of the inputs is copied to the output, determined by the selector lines)
	Timing (Hazards)	We will take a look at what can go wrong in a sum-of-products solution of a logic function. While the initial output value is 1 and the final steady-state output value is also 1, temporarily the output can be 0. This is a so-called static-1 0-glitch, and if it can occur a static-1 0-hazard. We will also see how to improve the circuit to eliminate such hazards.
	Memory (latch & flipflop)	When feedback is used in logic circuits, the emergent property can be that the circuit has memory; the output no longer only depends on the input, but also on the current state.
	Master/Slave Flip-flops	A master-slave flip-flop is made of two gated S/R latched placed in series. At the first halve of a clock cycle the master is processing the signal, while at the second halve the slave is processing.
	Master/Slave Flip-flops 2	A close look at an edge-triggered master-slave D-type flip-flop.
	Finite State Machines	A finite state machine has both a logic array and memory. Four types exist: 1) Mealy Machines (input, output and memory), 2) Moore Machines (sequencers) with output and memory but no input, 3) Boole Machines with input and output but no memory, and 4) Berkeley Machines with input and memory but no output. An example is given of a Moore Machine sequencer, a 3-bit counter based on T-type flipflop memory elements.
	Finite State Machines 2. S/R counter	Another look at a Moore Machine (Finite State Machine with no input). In this case an example of how to build a 2-bit counter with S/R flipflops
	FSM Mealy machine. Parity checker	We will take a look at a full Mealy machine (with input and output), namely a parity checker. First we design a state diagram: a circle for all states and draw arrows how the states can change with input. Then we decide for our hardware (how many and what type of flipflops to use for the state and output). And then we can implement the things just as we had done for a (non-input) Moore machine. An action table. An excitation table. The logic array via Karnaugh maps, etc.
	FSM, Edge Detector	Here we take a look at another full Finite State Machine (Mealy Machine) with input and output and memory, namely an edge detector.

Second half: Computer Architecture. Combining Digital Components:

Preview	Title	Description
	Road Map summary	We take a look at how computer architecture is placed in the tree of knowledge
	Digital Systems Summary 1/3	A summary of the block of lectures above
	Digital Systems Summary 2/3	A summary of the block of lectures above
	Digital Systems Summary 3/3	A summary of the block of lectures above
	Adders	Half adders and full adders as the cornerstone of computer calculations
	Ripple-carry adder	Ripple-carry adder. How to make an n-bit adder from full adders. And how to turn an adder into a subtractor
	Carry-look-ahead adder	To improve speed of calculation, instead of 32 full adders in a ripple-carry adder, we will use 8 carry-look-ahead adders of 4 bits
	Left/right Shift	How a left/right 1-bit shifter is made
	(DE)MUX	A multiplexer (MUX) and demultiplexer (DEMUX)
	(DE)CODER	A coder and a decoder
	Comparator	A 4-bit comparator: A=B, A<B and A>B
	Arithmetic and Logic Unit (ALU)	A look at the Arithmetic and Logic Unit (ALU)
	Central Processing Unit (CPU)	A close look at a Central Processing Unit (CPU)
	Control Logic	How does the control logic work inside a CPU
	Multiplication Russian-peasant algorithm	How to go from addition hardware to a multiplication algorithm. The Russian-peasant algorithm
	Division	A shift-compare-subtract algorithm to do divisions with simple hardware
	Karatsuba	Some advanced multiplication techniques. Karatsuba algorithm (dividing large 2m bit numbers into 2 m bit numbers and doing the multiplication with them) and the look-up-table algorithm, in fact done with only a table of squares
	Static/dynamic RAM	How a basic memory (RAM) chip works
	Combining memory chips	How to join memory chips to have larger memory size.
	Information	The philosophical/physical aspects of information. About the amount of information when receiving a message and the entropy of a message before sending it.
	Physical memory organization	The physical organization of memory
	Memory (Software aspects 1/4)	How is the memory in a computer organized logically
	Endianness	Endianness (Little endian vs. Big endian)
	Memory (Software aspects 2/4)	More logic aspects of memory organization are presented. Heap vs. stack. Recursivity. Garbage collection. Global pointer, frame pointer.
	Memory (Software aspects 3/4)	More aspects of memory organization. Paging. Virtual memory. Memory management unit (MMU). Assembly addressing methods
	Memory (Software aspects 4/4). Overlays	Memory overlays
	Memory: ROM	How ROM (read-only memory) is made and it is compared to static and dynamic RAM
	BIOS and bootstrapping	About the BIOS and how it can bootstrap the computer into action
	Buses and motherboards	How does the CPU communicate with other components? Here we will see the hierarchy of communication buses. We'll also take a look where all the components are on a Motherboard
	Communication	We will see here how in communication bit-errors can be avoided by hardware and software. hardware: twisted pair. Software: parity checking and forward-error correction (FEC) using Hamming 7.4 coding
	Floating point IEEE 754 (1/4)	How do we represent real numbers on a computer? In comparison to integer numbers.
	Floating point IEEE 754 (2/4)	With a limited number of digits, what are the ranges and precision of the numbers?
	Floating point IEEE 754 (3/4)	The IEEE 754 standard. How floating point numbers are represented in 32 bit (single) and 64 bit (double). Normalized and denormalized numbers. Fractions and significands. Exponent, excess-127
	Floating point (4/4). Divisions	How multiplications and divisions are done on a computer. Divisions consists of finding the reciprocal of the denominator
	Floating point: Newton Raphson method	How to implement other mathematical functions. Here we will see how to use the method of Newton-Raphson to find the square root of an argument.
	Architecture examples	A list of items to take into consideration when analyzing a computer architecture
	Difference Engine	A close look at how the Difference Engine of Charles Babbage looked (beginning of 19th century)
	Intel 4004	A short summary of the Intel 4004 processor. Bad sound!!!
	Intel 4004 (addendum)	Some extra features of the Intel 4004 processor described
	Intel 4004 (1/2)	A short summary of the Intel 4004 processor
	MOS 65xx (1/2)	It was used in the first Apple computers and the famous Commodore C=64, but how does the MOS 65xx family of CPUs work?
	MOS 65xx (2/2)	How a 65xx Assembly instruction is constructed and translated into machine code
	VICE C=64 emulator and Merlin Assembler	A C=64 emulator running an assembler to write programs in 6510 Assembly (Merlin)
	x86 (1/2)	A look at the Intel x86 family of processors
	x86 (2/2)	A look at the Intel x86 family of processors
	AVR Atmel (Arduino)	A close look at the AVR Atmel used in for instance the Arduino platform
	AVR Assembly	How to write AVR Assembly and upload it to an AVR processor in an Arduino board. We will use the avra assembler to translate our code and the avrdude program to upload it to our processor
	x86 Assembly Hello World (1/3): NASM	How to use the NASM compiler to write an x86 Assembly program to print "Hello World" using system calls and interrupts (0x80)
	x86 Hello World (2/3): AS	How to use the AS compiler to write an x86 Assembly program to print "Hello World!" using interrupts (0x80)
	x86 Assembly: Hello World (3/3): `printf`	How to use libraries from other languages in x86 Assembly. More specifically, how to use printf to output strings and integers
	x86 in-line Assembly in C	How to use in-line x86 Assembly in C code
	Quantum computing	What is quantum computing and how does it work?
	Asynchronous computing. The brain	The difference between synchronous and asynchronous computing. An example how the brain works and comparing it to the state-of-the-art Summit computer. Can it pass a Turing test?

Part 3: MIPS Assembly:

Preview	Title	Description
	MIPS Assembly intro	A presentation of the Assembly programming language as a bridge between computer-understandable machine language, like 011001001 and higher-level programming languages like C and Pascal, for (i=0; i<10; i++)
	MIPS Install MARS	How to install the MARS environment to develop MIPS Assembly programs
	MIPS architecture	A data flow diagram of the MIPS architecture to have a mental picture when we are programming MIPS
	MIPS Registers	We take a look at the 32 registers (each 32 bits wide)
	Hello World	A detailed look at a simple MIPS Assembly program. "Hello World"
	MIPS operations	A look at the instruction set of MIPS and an example of translating an Assembly instruction add $t2, $t1, $t0 to machine language (binary or hexadecimal)
	MIPS Instruction Set	A look at the instruction set. Being a RISC architecture, the range of available instructions is limited, and we take a brief look at all of them
	MIPS System calls	System calls are interrupts, temporarily transferring execution to the operating system to perform a task and then continue with the rest of the program. For instance input/output. Here it is described how it is done in MIPS. Moreover, we take a look at pseudo instructions like LA (load address) and LI (load immediate)
	If-then-else	How the C structure if-then-else is implemented in (MIPS) Assembly
	Mask & shift	How masking works (AND, OR, XOR) and how we have logic and arithmetic versions of shifting
	For loops	How to implement a for-loop in MIPS Assembly
	Memory instructions	What MIPS instructions do we have available to access main memory (outside CPU). As we will see variables do not exist. It is all pointers! As such, we can load a character from memory and add 1 to it, as if it were an integer, and then go back treating it as a char
	Structures and arrays	How structures and arrays are implemented in MIPS
	Functions (1/3) (jal, jr, $a, $v)	We convert a for-loop into a while-loop and then a construction with if-goto. Then we place the instructions inside the loop in a separate piece of code, a function. To increase flexibility, we pass the information to the function in $a registers and return values in $v registers. Moreover, to be able to call the function anywhere in the code, we need the jal (jump-and-link) instruction and return from the function by jr (jump register)
	Functions (2/3) Stack	How to use the stack to save and retrieve register values when using function calls. Push and pop
	Functions (3/3)	In the previous functions we learned how to use the combination of 'jal' and 'jr $ra' to implement functions. Then we learned how to take care of the registers by saving them on the stack. Now we look what happens if we have a function calling another function. We will see that also $ra has to be saved on the stack.
	Recursive functions	How to implement in MIPS recursive functions, functions that call themselves
	Floating point (1/2)	What floating-point instructions do we have available in MIPS Assembly?
	Floating point (2/2)	An example of a MIPS Assembly program using floating point calculation

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