Zoom 101

Zoom 102

MCS 260: Intro to Computer Science

• Instructor: Prof. Emily Dumas   ⟨edumas@uic.edu⟩
• TA: Jennifer Vaccaro   ⟨jvacca4@uic.edu⟩
• TA: David (Hai) Wang   ⟨hwang202@uic.edu⟩

Immediate action items

• Read the syllabus
  (Yes, the entire thing. Yes, it is boring.)
• Check the blackboard course site regularly.

Python

Python is a computer programming language.

• #3 most popular programming language in TIOBE
• Extensive use at Dropbox, Instagram, Netflix, ...
• #1 most popular (by far) in a 2018 survey of data science / machine learning professionals (source)

Live demo time

Number systems

Humans usually use the decimal number system, also known as base $10$.

In this system there is a $10^0=1$s place, a $10^1=10$s place, a $10^2=100$s place, etc.

There are $10$ digits with values $0, 1, \ldots, 9$.

In decimal, $312$ means: $${\color{red}3 \color{green} 1 \color{orange} 2} = {\color{red} 3} \times 10^2 + {\color{green} 1} \times 10^1 + {\color{orange} 2} \times 10^0$$

In computer science, three non-decimal number systems are often encountered.

• Binary, or base $2$.
• Hexadecimal, or base $16$.
• Octal, or base $8$. (Least common.)

Binary

The digits are $0$ and $1$. A binary digit is called a bit.

The place values are $1$, $2$, $4$, $8$, $16$, etc.

Example: $1001_2$ means $$1\times 8 + 0 \times 4 + 0 \times 2 + 1 \times 1 = 9$$

In Python, binary numbers are indicated by preceding the digits with $\texttt{0b}$.

So the previous example would be written $\texttt{0b1001}$.

We can convert to binary using integer division and remainder.

Integer division
$x /\!/ 2$ means $x$ divided by $2$, discarding the remainer.
e.g. $7 /\!/ 2 = 3$,   $6 /\!/ 2 = 3$.

Remainder
$x \texttt{%} 2$ means the remainder when $x$ is divded by $2$. $7 \texttt{%}2 = 1$, $6 \texttt{%} 2 = 0$.

To convert a number to binary, just keep track of the remainders when you repeatedly integer-divide by $2$.

So $312 = \texttt{0b}\color{#F00}{\texttt{1}}\color{#F02}{\texttt{0}}\color{#F04}{\texttt{0}}\color{#F06}{\texttt{1}}\color{#F08}{\texttt{1}}\color{#F0A}{\texttt{1}}\color{#F0C}{\texttt{0}}\color{#F0E}{\texttt{0}}\color{#F0F}{\texttt{0}}$, i.e. $312 = 256 + 32 + 16 + 8$.

Binary is not ideal for human consumption because of its low information density.

e.g. $9754 = \texttt{0b10011000011010}$.

Hexadecimal addresses this, giving a more condensed way of expressing a sequence of bits.

Hexadecimal

Hexadecimal or hex is a condensed representation of binary, with one symbol for each $4$-bit block.

Each $4$-bit block is just a number between $\texttt{0b0000}=0$ and $\texttt{0b1111}=15$. We use hex digits $0\ldots9$,$A \ldots F$:

Hexadecimal

Hexadecimal or hex is a condensed representation of binary, with one symbol for each $4$-bit block.

Each $4$-bit block is just a number between $\texttt{0b0000}=0$ and $\texttt{0b1111}=15$. We use hex digits $0\ldots9$,$A \ldots F$:

In Python notation, hexadecimal numbers begin with $\texttt{0x}$, followed by the digits.

So $\texttt{0x3e}$ means

Hexadecimal is also base $16$. Another way to see $\texttt{0x3e}$: $$\begin{align}\texttt{0x3e} &= \texttt{3} \times 16^1 + \texttt{e} \times 16^0 \\ &= 3 \times 16 + 14 \times 1 = 62 \end{align}$$

Aside: In decimal we sometimes separate groups of digits with punctuation for easier reading.

e.g. in the USA one million is often written "$1,\!000,\!000$".

In Python notation the underscore "$\texttt{_}$" can be used as a separator.

$$\begin{align}\texttt{0b1111_0100_0010_0100_0000} &= \texttt{0xf4240}\\ &= \texttt{1_000_000} \end{align}$$

When converting binary to hex, the number of bits may not be a multiple of $4$ at first. In this case we need to add some zeros on the left:

$$\texttt{0b10101} = \texttt{0b00010101} = \texttt{0b0001_0101} = \texttt{0x15}$$

To convert a decimal number to hex, one way is to convert to binary and group bits.

An alternative is to repeatedly integer-divide by $16$ and use the remainders:

Therefore $62 = \texttt{0x}\color{#F00}{\texttt{3}}\color{#F0F}{\texttt{e}}$