Binary Numbers Practice
A computer has exactly two things to work with: on and off, 1 and 0. Every
number, word, image, and video it handles is built out of just those two. Before
we build circuits that compute, we need to count the way a computer does.
Overview
In this lab you'll practice reading and writing numbers in binary (base-2), converting between binary and decimal (base-10), and adding binary numbers by hand.
You've got it when…
- You can convert a binary number to decimal.
- You can convert a decimal number to binary.
- You can add two binary numbers and carry correctly.
Collaboration & AI
Work: On your own. Compare answers with a neighbor to check yourself, but do the conversions by hand — that's the skill.
AI — AIAS Level 1, No AI: Work these out yourself so the place-value math becomes second nature. What the levels mean.
Recording your answers
Write your answers in your notebook (this page isn't a fill-in form). Copy each table and fill in the blank column.
Key Vocabulary
Make sure you can define each of these in your own words:
- Bit
- Byte
- Binary
- Decimal
- Base-2 / Base-10
- Place value
- Overflow
Conversion Practice
Convert the following binary numbers to decimal.
| Binary | Decimal (your answer) |
|---|---|
| 1001 | |
| 1110 | |
| 0101 | |
| 1101 |
Convert the following decimal numbers to binary.
| Decimal | Binary (your answer) |
|---|---|
| 7 | |
| 12 | |
| 19 | |
| 25 |
Binary Addition
Sum the following binary numbers.
| Binary addition problem | Binary sum (your answer) |
|---|---|
| 0110 + 0011 | |
| 1001 + 0100 | |
| 1100 + 1001 |
Challenge Questions
- How many different values can be stored in 5 bits?
- Why do computers use binary instead of decimal?
Turn It In
- Your completed conversion and addition tables, in your notebook.
- Your answers to the two challenge questions.
How It's Graded
This lab is worth up to 4 points. One score covers everything you turn in.
| Score | What it looks like |
|---|---|
| 4 — Excellent | Every conversion and sum is correct, your work shows how you got there (place values or the subtraction steps, not just answers), and both challenge questions are answered with a reason, not a guess. |
| 3 — Above Average | All tables and questions are complete and the method is visible, with a few arithmetic slips — a missed carry, a misread column. |
| 2 — Average | Everything is attempted, but several answers are wrong or the work shows answers only, with no visible method to check. |
| 1 — Below Average | Noticeable gaps — a table or the challenge questions left unfinished, or most conversions incorrect. |
| 0 — Failing | Nothing in the notebook, or too little to tell whether you practiced. |