# Learning Objectives

### CLO

Upon successful completion of this course, students will be able to:
1. Understand digital logic and how it is used to build a computer system.
2. Explain how CPU functions to run a software program.
3. Develop assembly programs to control the operation of the CPU.
4. Understand the format of instructions and their operations.
5. Understand the role of the other components of a computer system such as buses and memories and how
they work together.

Lecture plan:

• Number System (CLO 1)
• Binary
• Hex
• ASCII
• Units (CLO 1)
• Kibibytes, Kilobytes etc.
• Hardware Architecture (CLO 2)
• Data bus
• Microcontrollers
• On-chip peripherals review
• Compilers and Programming Languages (CLO 3, CLO 4)
• Compiled vs. Interpreted languages
• C compiler
• Hands-on with a compiler

# Reference Material

Reference Material

# Tools

In the past, we needed to setup special tools on a local computer (i.e.: your laptop) to test software. In the modern era, the advanced made by software developers have led us to several tools we can use to understand a machine's instruction set.

1. Python Interpreters
2. MIPS Emulators
3. Logic Emulators
Reference Material

# Books and Online Resources

Really awesome book from Robert Plantz:

Books:

Online Resources

Basics

# Number Systems

### Number Types

The number system holds significance in terms of writing and expressing code to a computer, typically in a programming language. Note that we (as humans) do not use hex or binary numbers that much outside of the computer science domain. For example, we don't walk into a supermarket and read prices in binary such as `\$0x10` :)

Often times in programming, we need to express numbers more quickly, and we might say int `x = 0x10000000` to quickly indicate 32-bit value with `bit31` set to 1. Notation `x = 0x10000000` is easier than writing `x = 268435456` which would be more cryptic for a programmer to realize the significance of because the reader of the programming code will not be able to quickly realize that it is specifically setting `bit31` to value of `1`.

#### Decimal

Typical numbers we are familiar with are decimals which are technically "base 10" numbers. So an ordinary number that we may be aware of such as 123 can be written as 12310.

The number 123 could also be written as:

`1*102 +2*101 +3*100` which is equal to `100 + 20 + 3 =12310`

#### Binary

Binary numbers are always 1s and 0s only. Similar to decimal numbers, binary numbers increase in powers of 2, rather than powers of 10. Binary numbers are written by with the "0b" notation, such as 0b1100

For example, binary `101` or `0b101` can be written as:

`1*22 +0*21 +1*20` which is equal to `4 + 0 + 1 = 510`

#### Hex

One digit of a hex number can count from 0-15, but since we have to represent the hex number using a single character, the numbers 0-9 are usual numbers, and the numbers 10-15 are represented by A, B, C, D, E, F

Where decimal is a power of 10, and binary is power of 2, hex numbers are powers of 16. Hex numbers are written with the "0x" notation, such as 0x10.

For example, hex `0x12` can be written as:

`1*161 +2*160` which is equal to `16 + 2 = 1810`

As another example, hex `0xC5` can be written as:

`12*161 +5*160` which is equal to `192 + 5 = 19710`

### Exercises

#### Decimal to Binary

Decimal (base 10) numbers can be converted in a couple of different ways as described here. One of the methods is to continue dividing by 2 and note down the remainder as described in the image below. The article above also describes a potentially faster method of conversion so be sure to read it! Please try converting the following to binary:

1. 125
2. 255
3. 500

#### Decimal to Hex

Decimal to hex is similar to Decimal to Binary except that we are dealing with powers of 16 rather than powers of 2.

My favorite method of conversion from decimal to hex is to first convert the number to binary. For example, let's start with a large number such as 23912. We can use the Decimal to Binary method to convert this first to binary:

• `2391210`
• `0b101110101101000`
• Split it up to nibbles:
• `0b101 1101 0110 1000`
• Then use the lookup table listed in Hex to Binary:
• `0x5D68`

Please try converting the following to hex:

1. 125
2. 255
3. 500

#### Hex to Binary

The following table can be utilized to convert hex to binary very instantly:

 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 xA xB xC xD xE xF 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

First row is HEX, and the second row is binary. For whatever hex number we wish to convert, we simply locate its equivalent in binary. For instance, if we wish to convert `0x5` to binary, it is `0b0101`, and `0xA5` would be `0b1010.0101` as you can convert one "nibble" (4-bits) at a time.

Let's take another example to convert `0x1BF` to binary; simply break it down by "nibbles":

• `0x1` --> `0b0001`
• `0xB` --> `0b1011`
• `0xF` --> `0x1111`
• Answer: `0b0001 1011 1111`

Please try converting the following to binary:

1. 0x55
2. 0x125
3. 0x40000000

#### Hex to Decimal

For Hex to Binary, we used a lookup table as a "cheat code" :). For Hex to decimal, it would be easier to re-write the numbers as powers of 16. For example, to convert `0x1BF` to decimal, we can break it down to:

• `0x1` --> `1 * 162` --> `256`
• `0xB` --> `11 * 161` --> `176`
• `0xF` --> `15 * 160` --> `15`
• `256+176+15 = 447`

Please try converting the following to decimal:

1. 0x55
2. 0x125
3. 0x40000000

Basics

# Python Number Converter

Generally speaking, practiced skill cannot be easily forgotten. It is far better to go through the process and practice converting a number, rather than to memorize the process.

Before we get started, have a look at the Tools Page to get started with a Python Interpreter we could use for this exercise.

### Number to Printable Hex

``````def nibble_to_ascii(nibble: int) -> str:
"""
This is a comment
Input: Nibble (4-bits)
Output: Single character HEX as a string
Example: Input = 10, Output = 'A'
Example: Input = 8,  Output = '8'
"""
table = ['0','1','2','3','4','5','6','7','8','9','A','B','C','D','E','F']
return table[nibble]

def to_hex(number: int) -> str:
"""
This is a comment
Input: Number (integer)
Output: String
Example: Input = 43605, Output = "0xAA55"
"""

# Forever loop
while True:
# Integer divide using the // operator
quotient = number // 16
# Get the remainder using the % operator
remainder = number % 16

# Accumulate result

# Set the number we need to use for next time
number = quotient

# We break the "loop" when division turns to zero
if (quotient == 0):
break

print(to_hex(123456789))
print(to_hex(0b1010101))
Write a function `to_binary()` that takes a number, and returns the string equivalent version of the number in binary. You can borrow the template above of `to_hex()` function and most of the logic might be similar except that we would be dividing number by 2 rather than 16.