Topic 1b — Binary and Hexadecimal Integer Representation

Learning Objectives

By the end of this topic, you should be able to:

• Convert an unsigned binary integer to its equivalent base‑10 (decimal) value.
• Convert a base‑10 integer to its equivalent unsigned binary representation.
• Convert a 4‑bit (nibble‑length) binary value to its equivalent hexadecimal digit.
• Convert a hexadecimal digit to its equivalent 4‑bit binary value.

Learning Activities

To help you meet the learning objectives, we have prepared a combination of readings, activities, and videos.

Course Readings

These reading were designed to introduce the course topics to an audience of educators. They should be considered "required" and read in order.

• Reading 1: Bits, Bytes, and Abstractions (conceptual foundations)
• Reading 2: 8 Bits and the Integers 0–255 (binary place value and conversions with one byte)
• Reading 3: Hexadecimal: A Shorthand for Binary (conversions between 4‑bit groups and hex digits)

Supplemental Readings

Some participants find it helpful to read about a topic from a source written for a slightly more technical audience. These supplemental readings cover similar material as the course readings but may not fully align with the course learning objectives. Use them as an optional complement to your study, not a substitute for the course readings.

• Reading: Dive into Systems, Chapter 4, Binary and Data Representation
• Reading: Dive into Systems, Chapter 4.1, Number Bases and Unsigned Integers
• Reading: Dive into Systems, Chapter 4.2, Converting Between Bases

Lesson Videos

These videos support the readings above and may present the material with some deeper connections and/or worked examples.

• VIDEO: Converting binary strings to integers
• VIDEO: Converting integers to binary strings (left to right)
• OPTIONAL VIDEO: Converting integers to binary strings (right to left)
• VIDEO: Let's talk about Hex baby

Checking for Understanding, Questions

Review the Learning Objectives from the top of this page. You will be asked to complete these types of problems on this week's competency demo. To help you check if you are on the right track with these concepts, use the following tools and questions as a type of formative self-assessment.

First, the following are two Scratch programs to help you practice conversion from decimal to binary and back again.

• Practice converting from binary to an unsigned integer
• Practice converting from an unsigned integer to binary

Next, consider the following questions. Try each one on your own before looking at the answer key. It is completely fine if you need to revisit the reading or video — that’s part of learning.

Binary → Decimal

1. What base‑10 value does the 8‑bit binary number 01010011 represent?
2. What base‑10 value does 11100001 represent?

Decimal → Binary (8‑bit, unsigned)

3. Write the 8‑bit binary representation of the decimal number 19.
4. Write the 8‑bit binary representation of the decimal number 200.

Binary ↔ Hexadecimal

5. Convert the 4‑bit binary value 1010 to hexadecimal.
6. Convert the hexadecimal digit D to its 4‑bit binary equivalent.
7. Convert the 8‑bit binary number 10111100 to hexadecimal (two hex digits).
8. Convert the hexadecimal value 3F to its 8‑bit binary equivalent.

How Many Values with N Bits?

9. How many unique values can you represent with 8 bits?
10. How many unique values can you represent with 10 bits?
11. In general, how many unique values can you represent with N bits?

Checking for Understanding, Answers

You can begin be comparing your answers to the following answer key.

If you still have questions or concerns you can use the videos below to try and further your understanding.

• VIDEO: Binary → Decimal walkthrough
• VIDEO: Decimal → Binary walkthrough
• VIDEO: Binary ↔ Hexadecimal walkthrough
• VIDEO: How Many Values with N Bits? walkthrough

Extend Your Learning