Logo Lectures: Computer Architecture
on Youtube

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

Computer Architecture. Digital systems:

On existence
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
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
Number Conversions
How to convert numbers from any number base to any other number base.
Negative Numbers
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
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
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
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
Sum of Products
Product of Sums
How to implement any logic function with only AND, OR and NOT operations.
Karnaugh Maps
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
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)
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.
latch and flipflop 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
Master/Slave Flip-flops 2
A close look at an edge-triggered master-slave D-type flip-flop.
Finite State Machines
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
                  Machine 2: S/R counter
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
                  machine: parity checker
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.
Edge Detector
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:

Road Map summary
Road Map summary
We take a look at how computer architecture is placed in the tree of knowledge
Digital Systems Summary
Digital Systems Summary 1/3
A summary of the block of lectures above
Digital Systems
Digital Systems Summary 2/3 A summary of the block of lectures above
Digital Systems Summary
Digital Systems Summary 3/3 A summary of the block of lectures above
Adders Adders
Half adders and full adders as the cornerstone of computer calculations
Ripple-carry adder
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
L/R Shift
Left/right Shift
How a left/right 1-bit shifter is made
A multiplexer (MUX) and demultiplexer (DEMUX)
(DE)CODER A coder and a decoder
Comparator, 4 bit: A=B, A<B, A>B
A 4-bit comparator: A=B, A<B and A>B
Arithmetic and Logic Unit
Arithmetic and Logic Unit (ALU)
A look at the Arithmetic and Logic Unit (ALU)
Central Processing Unit (CPU)
Central Processing Unit (CPU)
A close look at a Central Processing Unit (CPU)
Control Logic
Control Logic
How does the control logic work inside a CPU
Multiplication: Russian-peasant algorithm
Russian-peasant algorithm
How to go from addition hardware to a multiplication algorithm. The Russian-peasant algorithm
A shift-compare-subtract algorithm to do divisions with simple hardware
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 Static/dynamic RAM
How a basic memory (RAM) chip works
Combining memory
                  chips Combining memory chips
How to join memory chips to have larger memory size.
Information 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.
                  organization Physical memory organization
The physical organization of memory
                  (Software aspects 1/4) Memory (Software aspects 1/4)
How is the memory in a computer organized logically
Endianness Endianness
Endianness (Little endian vs. Big endian)
                  (Software aspects 2/4) Memory (Software aspects 2/4)
More logic aspects of memory organization are presented. Heap vs. stack.  Recursivity. Garbage collection. Global pointer, frame pointer.
                  (Software aspects 3/4) 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 (Software aspects 4/4). Overlays
Memory overlays
Memory: ROM Memory: ROM
How ROM (read-only memory) is made and it is compared to static and dynamic RAM
BIOS and
                  bootstrapping BIOS and bootstrapping
About the BIOS and how it can bootstrap the computer into action
Buses and
                  motherboards 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 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
                  point IEEE 754 (1/4) Floating point IEEE 754 (1/4)
How do we represent real numbers on a computer? In comparison to integer numbers.
                  point IEEE 754 (2/4) Floating point IEEE 754 (2/4)
With a limited number of digits, what are the ranges and precision of the numbers?
                  point IEEE 754 (3/4 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
                  point (4/4). Divisions 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 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.
                  examples Architecture examples
A list of items to take into consideration when analyzing a computer architecture
Difference Engine Difference Engine
A close look at how the Difference Engine of Charles Babbage looked (beginning of 19th century)
Intel 4004 Intel 4004
A short summary of the Intel 4004 processor. Bad sound!!!
Intel 4004
                  (addendum) Intel 4004 (addendum)
Some extra features of the Intel 4004 processor described
Intel 4004 (1/2) Intel 4004 (1/2)
A short summary of the Intel 4004 processor
MOS 65xx (1/2) 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) MOS 65xx (2/2)
How a 65xx Assembly instruction is constructed and translated into machine code
x86 (1/2 x86 (1/2)
A look at the Intel x86 family of processors
x86 (2/2) x86 (2/2)
A look at the Intel x86 family of processors
AVR Atmel (Arduino) AVR Atmel (Arduino)
A close look at the AVR Atmel used in for instance the Arduino platform
                  Assembly Hello World (1/3): NASM 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 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 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

Part 3: MIPS Assembly:

MIPS Intro
MIPS Assembly intro A presentation of the Assembly programming language as a bridge between computer-understandable machine language, like
and higher-level programming languages like C and Pascal,
  for (i=0; i<10; i++)
How to install MARS
Install MARS
How to install the MARS environment to develop MIPS Assembly programs
MIPS Architecture
MIPS architecture
A data flow diagram of the MIPS architecture to have a mental picture when we are programming MIPS
MIPS Registers
MIPS Registers
We take a look at the 32 registers (each 32 bits wide)
MIPS Hello World
Hello World
A detailed look at a simple MIPS Assembly program. "Hello World"
MIPS operations
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
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
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)
MIPS If-then-else
How the C structure if-then-else is implemented in (MIPS) Assembly
Mask & Shift
Mask & shift
How masking works (AND, OR, XOR) and how we have logic and arithmetic versions of shifting
For loops For loops
How to implement a for-loop in MIPS Assembly
Memory instructions 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 &
                  arrays Structures and arrays
How structures and arrays are implemented in MIPS
Functions (1/3) 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) Functions (2/3)
How to use the stack to save and retrieve register values when using function calls. Push and pop
Functions (3/3) 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 Recursive functions
How to implement in MIPS recursive functions, functions that call themselves
Floating point
                  (1/2) Floating point (1/2)
What floating-point instructions do we have available in MIPS Assembly?
Floating point
                  (2/2) Floating point (2/2)
An example of a MIPS Assembly program using floating point calculation