Practice Binary, Octal and Hex Conversions for CS Exams

The four bases you will meet

Decimal is base 10, binary base 2, octal base 8 and hexadecimal base 16, where the digits A to F stand for 10 to 15. In code you will see prefixes: 0b for binary, 0 or 0o for octal and 0x for hex. A single value shows how they relate: decimal 255 is 11111111 in binary, 377 in octal and FF in hexadecimal.

Method 1: decimal to binary

Divide the number by 2 repeatedly and write down the remainders, then read them from the last to the first. For 45, the remainders are 1, 0, 1, 1, 0, 1 from first to last division, so 45 is 101101. Check it with place values: 32 + 8 + 4 + 1 = 45.

Practice loop

1. Pick a decimal number between 1 and 255 at random.
2. Convert it to binary by hand and write your answer.
3. Group the bits in fours from the right to get hexadecimal, or in threes to get octal.
4. Paste the decimal number into the converter and compare all three results.
5. If something differs, find the first digit where your work diverges and note why.
6. Repeat with larger values. If your syllabus includes fractions or negative numbers, work those by hand, because the converter handles whole numbers.

Shortcuts examiners like

• Each hex digit equals exactly four bits, so 0xA7 is 1010 0111.
• Each octal digit equals exactly three bits, so 755 is 111 101 101, the Unix permission rwxr-xr-x.
• Powers of two are worth memorizing up to 2^10 = 1024.
• A binary number ending in 0 is even; ending in 1 is odd.
• Subnet masks use the pattern: 255 is 11111111, 252 is 11111100, 192 is 11000000.

Where it shows up in networking and programming

Networking exams love IPv4 addresses and masks. The address 192.168.1.10 is 11000000.10101000.00000001.00001010 in binary. Converting each octet separately is the standard approach for subnet questions. In programming courses, you will see hex for colors such as #FF8800, memory addresses and bit masks, and octal for file permissions.

Negative integers use two's complement in most course material. For 8 bits, -1 is 11111111, and to negate a number you invert the bits and add one. The converter shows a negative number with a minus sign rather than as two's complement bits, so work signed values by hand and be careful when comparing answers with your textbook.

Common mistakes to watch for

Students often write binary results in the wrong order, drop leading zeros when a question asks for a fixed width such as 8 bits, or forget that hex letters can be lower or upper case but represent the same value. Another trap is mixing the prefix with the digits: 0x1F is 31, but 1F by itself has no meaning without a stated base. Read each question for the required width and base before you start, and write the base as a subscript when you can, for example 1011 with a small 2 beneath it.

Use the tool as a checker, not a crutch

Do the first five practice problems without it, then verify in a batch. In the exam you will not have a converter, so the goal is speed with accuracy. Keep a list of the mistakes you repeat, such as reading remainders in the wrong order, and review that list the night before.