Hexadecimal

This is a free interactive resource to help you investigate and develop your hexadecimal to denary conversion skills.

You are probably familiar with the idea that the same number can be written down in different ways - as a tally, as a normal digital, as a roman numeral, or even as binary (which appears in the KS3 National Curriculum for Computing). Hexadecimal is a number system that's based on 16s - it's also known as base 16.  It's useful in computing for representing large numbers concisely (and also because it's easily converted to binary). Hexadecimal appears in most GCSE Computer Science courses, which usually require you to convert between denary and hexadecimal.

In a number system based on tens, each column heading (units, tens, hundreds, etc.) is ten times the value of the column heading to its right, and you can use one of ten values (1-9 and 0) in each position. In a number system based on sixteens, each column heading is sixteen times the one to its right, and you can use one of sixteen values in each position.

There aren't sixteen different digits, though, so what comes after 9? Well, hexadecimal uses the digits 0-9, followed by the letters A-F. This means that counting in hexadecimal would give the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, etc.

You can click the digits below investigate how to make a hexadecimal number. Clicking each digit with the left mouse button increases it by one, and when it gets to 15, it goes back to 0. Clicking the right mouse button (or a long-tap on a touch-screen) decreases the digit by one.

If you change the hexadecimal number so that it reads 00A4, for example, that means that you want ten 16s and four 1s, so the value of 00A4 is 164. It's as simple as that! If you find the letters confusing, you could try starting with the abacus (in base 16).

Click the digits to investigate. Can you make 100? Is there only one pattern of digits that make each number? As you can see, hexadecimal numbers get big quite quickly. What's the maximum value that you can store in a four-digit number like the one above? Does that number look familiar?

Hexadecimal numbers are most commonly used in Computing to represent colours on web-pages, in drawing applications and in programming. GCSE Computer Science requres you to know how to convert directly between binary and hexadecimal.

For a more in-depth discussion of number bases, look at the Number Bases page in the Mathematics section.  You can also watch videos on number bases on the AdvancedICT YouTube channel.