Signed vs. Unsigned Binary: Those Tricky Numbers!

We're diving into the murky world of binary numbers. You know, those ones and zeros that computers love to chew on? Well, it turns out they're not all the same. We've got signed and unsigned binary, and they're about as different as a peas you are about to eat and peas you have passed.

Unsigned binary? Easy peasy. It's all positive, like a puppy with a bone. But signed binary? That's where the trouble starts. See that first bit, the one on the left? If it's a 1, BAM, you've got a negative number. Like a digital slap in the face.

Now, you might be thinking, "Why bother?" Well, in exams, they love to throw this at you. They'll ask if a number is signed or unsigned. If they don't tell you, just assume it's unsigned. Better safe than sorry, eh?

Negative Numbers in Binary: Not as Scary as Your Brother's Toenail Collection

Right then, buckle up buttercups, because we're plunging headfirst into the slightly bonkers world of representing negative numbers in binary. You know, those strings of ones and zeros that make computers tick (and sometimes throw a digital tantrum).

Now, you might think binary is all sunshine and rainbows, counting upwards like a well-behaved toddler. But hold your horses! We've got ways to show the naughty numbers too – the ones below zero. Two main methods for this trickery are sign and magnitude and that fancy-pants two's complement.

Listen up, because exam time loves a bit of this! Usually, the folks marking your hard work will tell you which method is being used. If not, and they want you to go negative, they'll probably give you a nudge in the right direction. So, keep your peepers peeled!

Sign and Magnitude: A Bit of a Give-Away!

So, first up in our negative number shenanigans is something called 'sign and magnitude'. It's about as subtle as a slap with a wet fish.

Check out the very first bit on the left – the big cheese of the binary bunch. This little fella doesn't actually count towards the number itself. Nope! It's purely there to tell you if the number is playing nicely (positive) or being a right menace (negative).

If that first bit is a big fat 1, then BOOM! You've got a negative number on your hands. Think of it as a tiny digital warning sign. But if it's a nice, round 0, then you're in positive territory – as cheerful as a pig in muck.

Now, here's the sneaky bit. When you're actually working out the value of the number, you completely ignore that first 'sign' bit if it's a 1. Just pretend it's not even there and treat the rest of the binary like your regular, run-of-the-mill base 2 stuff. Easy peasy, right? Well, mostly...