In my previous post we learnt the fundamental concepts of how binary could be used to represent real numbers (i.e. numbers with a fractional component). When it comes to storing these numbers though there are two major approaches in modern computing. These are Fixed Point Notation and Floating Point Notation.In today’s post, we continue to build our background computer … [Read more...]

## You Put a Hex on Me – A Quick Guide to Hexadecimal Numbers

Beyond the Decimal and Binary numbering systems, Hexadecimal is the next most commonly used number base in computer science. In today’s post we take a look at this multi-purpose number base, examining the similarities between it and the aforementioned number bases of binary and decimal before learning some tricks in how to convert numbers to and from hexadecimal notation. … [Read more...]

## Divide and Conquer: A Four Step Process To Simplify Binary Division

Division is probably the hardest of the four basic arithmetic operations. In this post we walk through an easy to follow, step-by-step process that you can use to divide any two binary numbers. … [Read more...]

## Why Binary Multiplication May Not Be As Complicated As You Think

Welcome to the next post in my series on binary numbers and binary arithmetic. In todays post we’re again going to build on what we have learnt in my previous posts on binary addition and binary subtraction and see how we can perform multiplication in binary. … [Read more...]

## How To Convert Between Binary and Decimal Fractions

In previous posts we've seen how we can convert whole numbers from decimal to binary notation and back again but in all my posts so far we've only looked at integer (or whole) numbers. What if we wanted to represent real numbers instead? What if we wanted to represent numbers with fractional parts? In todays post we take a look at binary and decimal fractions. … [Read more...]

## Binary Overflow

Before we move on, I just wanted to take a moment to look at another peculiarity of using binary numbers, the concept of wrap-around. … [Read more...]

## The Secret To How Computers Perform Binary Subtraction

Now, we have already talked about how to perform binary addition but what about the opposite? How do we subtract two binary numbers? In today's post, we're going to walk through a couple of step-by-step examples. … [Read more...]

## Binary Sign Extension

A quick post today, explaining the concept of binary sign extension. Imagine the scenario. You have been using a single byte to store values and now want to extend this to store larger numbers? What would you have to do to extend your original 1-byte of data to now store numbers using 2-bytes? This is where binary sign extension comes in. … [Read more...]

## Signed Numbers in Binary

If you have been reading any of my previous posts, by now you should be becoming a bit more comfortable with binary numbers. Up until this point though, we’ve been talking about only positive numbers. The logical question that follows is what do we do for negative numbers? In todays post we’re going examine this question and look at signed numbers (numbers … [Read more...]

## Binary Addition

Ready for your next dose of background Computer Science knowledge? In today’s post we build on what we have learnt in my previous post and look at binary addition. … [Read more...]