• Understand different number systems
• Convert different number systems

Digital Defense League – Intro to Binary, Octal, and Hexadecimal Systems

Zuri, a college student who has a passion for cybersecurity, just started a new internship at a local cybersecurity firm. She has just been assigned to the “Digital Defense League”, a special unit responsible for the protection of the digital space in her area. She has been given three critical tasks, each requiring understanding and application of a different number system: Binary (Base-[latex]2[/latex]), Octal (Base-[latex]8[/latex]), and Hexadecimal (Base-[latex]16[/latex]). Let’s take what you just learned about positional systems and bases and help Zuri with her new tasks.

 

Before we dive in, let’s take a moment to explore these number systems a bit more.

• Binary (Base-2) System: The binary system is used in virtually all digital systems and is at the core of computing. It uses only two digits, [latex]0[/latex] and [latex]1[/latex]. Each digit position represents a power of [latex]2[/latex].
• Octal (Base-8) System: The octal system uses digits from [latex]0[/latex] to [latex]7[/latex]. It’s often used in computer programming as it provides a shorthand way of representing binary numbers since each octal digit represents three binary digits.
• Hexadecimal (Base-16) System: The hexadecimal system uses sixteen distinct symbols, [latex]0-9[/latex] and [latex]A-F[/latex], where [latex]A[/latex] to [latex]F[/latex] represent the numbers [latex]10[/latex] to [latex]15[/latex]. Hexadecimal is commonly used in programming and computer engineering because it’s convenient for representing binary code and is human-friendly.

The base-[latex]10[/latex] and base-[latex]16[/latex] systems share the same numerical representation up to [latex]9[/latex]. In both systems, the number [latex]9[/latex] is represented as [latex]9[/latex]. However, when we reach the number [latex]10[/latex], the hexadecimal system introduces a new convention. Instead of using a single digit, base-[latex]16[/latex] utilizes the letters [latex]A[/latex] to [latex]F[/latex] to represent the values [latex]10[/latex] to [latex]15[/latex], respectively. For example:  [latex]A[/latex] represents [latex]10[/latex], [latex]B[/latex] represents [latex]11[/latex], and so on.

Having introduced these systems, let’s get back to helping Zuri.

Critical Task 1: Binary Bank Break-In

Zuri’s first task is to help Binary Bank. Binary Bank uses a binary (Base-2) system to protect its vaults. A suspicious binary code from the bank’s logs has been discovered. They suspect it might be a password attempt from an unauthorized user. In order to understand the potential threat to Binary Bank’s system Zuri needs to convert the binary code from the login to base-[latex]10[/latex].

By deciphering the potential password attempt, Zrui managed to stop a possible break-in at Binary Bank!