CPSC 110-08: Computing on Mobile Phones Spring 2012 Homework: Binary and Hexadecimal Numbers Due: Monday 2/6 (before class)

CS Principles

• 5b. Explanation of how number bases, including binary and decimal, are used for reasoning about digital data.

Introduction

As we've discussed, binary sequences are an important way to represent digital data. Our number system, which we call the decimal system, is a base-10 number system. It uses 10 digits -- 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 -- and the places in a decimal number are based on powers of 10 -- i.e., the ones place (10⁰), tens place (10¹), hundreds place (10²), and so on.

The binary system is a base-2 system. It uses just 2 digits -- 0 and 1 -- and the places in the number are based on the powers of two. So we have the ones place (2⁰), the twos place (2¹), the fours place (2²), and so on.

Because binary numbers can get very long, computer scientists use other number systems based on powers of 2 that make it easier to represent digital data. One of these is the hexadecimal system, which is a base-16 system. It has 16 digits -- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. And the places in a hexadecimal number are based on powers of 16. So we have the ones place (16⁰), the sixteens place, (16¹), the 256-place (16²) and so on.

In this homework you will watch three short (10 minute) videos about binary and hexadecimal numbers and learn how to convert from one to the other.

Khan Academy Videos

Watch the following three Khan Academy videos on number systems. Salman Khan has a very nice way of presenting these ideas.

• Binary numbers
• Decimal, Binary, and Hexadecimal
• Number Base Conversions

Quiz Yourself

• Binary to Decimal
• Decimal to Binary
• Hexadecimal to Decimal
• Decimal to Hexadecimal
• Binary to Hexadecimal
• Hexadecimal to Binary

Getting Help

In Class