Information inside the computer

True or false? Justify each answer: (a) a bit can only be $0$ or $1$; (b) a byte consists of $10$ bits; (c) computers work in binary because their circuits only distinguish two states; (d) using the standard classroom convention, $1\ \text{KB}$ are $1000$ bytes.

Explain in your own words why computers use the binary system instead of our ten digits. Use the idea of a light switch, which can only be off or on, and the millions of tiny switches inside a processor to help you.

A bit is like a light bulb that can only be off ($0$) or on ($1$). How many "light bulbs" are needed to form a byte? Draw eight light bulbs in your notebook representing the byte $01100001$ and explain what each one means.

You can do it on paper and send a photo with your answer.

Explain why a computer does not directly store letters, colors or sounds, but zeros and ones: what the transistors in its circuits have in common with a light switch and what advantage working with only two possible states offers.

Match each unit to its definition: (a) bit, (b) byte, (c) kilobyte, (d) gigabyte. Definitions: 1. group of $8$ bits; 2. the smallest unit of information, a $0$ or a $1$; 3. using the school convention, $1024$ megabytes; 4. using the school convention, $1024$ bytes.

The figure shows eight boxes that together form a byte: seven already have a value and the last one is covered with a question mark, as shown in the diagram.

Which two values could the covered box hide? How many bits make up a byte? Write a byte created by you with its eight digits and explain what each box represents.

In the code computers use for text, each letter takes up $1$ byte. Calculate how many bytes the word "HOLA" takes up and how many bits that is in total, and explain the calculation you made.

Match each file to the most reasonable size: (a) a short text message, (b) a photo taken with a cell phone, (c) a song, (d) a movie. Sizes: 1. around $4\ \text{MB}$; 2. more than $1\ \text{GB}$; 3. a few bytes; 4. around $8\ \text{MB}$. Explain which of the four you based on your own experience.

Order these units from smallest to largest: megabyte, bit, gigabyte, byte, terabyte, kilobyte. Then explain, using the school convention $1\ \text{KB} = 1024\ \text{bytes}$, the relationship between each unit and the next one in the list.

The figure shows the ladder of information units: each step is climbed by multiplying, but the last step has lost its name, as shown in the diagram.

Which unit is missing from the last step? Write the full chain of equivalences from the bit up to that unit using the school convention ($1\ \text{KB} = 1024\ \text{bytes}$ and the same when going up to each larger unit) and explain in your own words why the step from bit to byte is different from the others.

A cell phone photo takes up $4\ \text{MB}$. Using the school convention ($1\ \text{GB} = 1024\ \text{MB}$), calculate how many photos fit into $1\ \text{GB}$ and how many into $64\ \text{GB}$, and explain why in practice slightly fewer fit than calculated.

Mara's cell phone has a capacity of $64\ \text{GB}$. In the storage settings, it details: Operating system $12\ \text{GB}$, Apps $20\ \text{GB}$, Photo gallery $28\ \text{GB}$, and Free space $4\ \text{GB}$. To install a critical update, the device requires having at least $10\ \text{GB}$ free. Mara states: "By deleting $150$ photos of about $7\ \text{MB}$ each, I will already have enough space by adding the $4\ \text{GB}$ of free space I have left."

1. a) Numerically prove, using the school convention ($1\ \text{GB} = 1024\ \text{MB}$), why Mara's statement is incorrect and determine how many photos of that size she would actually need to delete to obtain the $6\ \text{GB}$ she is missing.
2. b) Justify two alternative technical solutions that allow her to free up that space without having to delete any of her photos from the phone.