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binary numbers

🐧 The Penguin Café Presents ❄️

Binary Numbers (or: "Why Penguins Only Count in 0s and 1s") 🐟

The Penguin Café is packed today. Snowflakes drift past the windows, mugs of hot krill cocoa steam on the tables, and Chef Pebble bangs a spoon against an ice cup.

Chef Pebble: "Alright everyone, flippers off the pastries! Today's talk is about numbers. Not fish. Not pebbles. Binary numbers."

Gini and Karl slide to the front, knocking over Flip and Flipflop on the way. Pip is already asleep. Penguin Waddle is counting chairs. In binary.

Gini: "Humans use ten fingers, so they count in base 10."
Karl: "Penguins have flippers. We count in fish."
Gini: "And computers?"
Karl: "They only understand 0 and 1."

Chef Pebble nods wisely. "Zero fish. Or one fish. A perfect system."

In binary, every position is a power of 2. Karl calls them "magic ice blocks." Each block is either frozen (1) or missing (0).

2⁸	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
256	128	64	32	16	8	4	2	1

Flip: "So how do we turn binary into normal numbers?"
Gini: "Easy! We melt the ice blocks and add them up."

It's easy to convert from binary to decimal:
101 = 1*2⁰+ 0*2¹+1*2²= 1 +0+4=5

Penguin Waddle: "That's five fish."

011 = 1*2⁰+ 1*2¹+0*2²= 1 + 2 =3

Pip (waking up): "Three fish? I'm listening."

101010 = 0*2⁰+ 1*2¹+0*2²+1*2³+ 0*2⁴+1*2⁵= 2+8+32=42

Karl: "42 fish. The meaning of life." Everyone nods.

Chef Pebble: "And what if we start with a normal number?"
Gini: "Then we divide. Again. And again. Until the number gives up."

To convert decimal numbers into binaries is a bit more tricky: To convert decimal numbers into binaries is a bit more tricky:
Let's start with 12:

12 = 2 * 6 + 0
6 = 2 * 3 + 0
3 = 2 * 1 + 1
1 = 2 * 0 + 1

(to find the right numbers, divide 12 by 2, take the result, 6 in this case and again divide by 2 until you have reached 1)

Now you take the remainder starting at the bottom and you have the binary number.
12 = 1100.

Another example:

42 : 2 = 21 + 0
21 : 2 = 10 + 1
10 : 2 = 5 + 0
5 : 2 = 2 + 1
2 : 2 = 1 + 0
1 : 2 = 0 + 1

So as we have already seen above 42 = 101010.

And one more example:
123 : 2 = 61 + 1
61 : 2 = 30 + 1
30 : 2 = 15 + 0
15 : 2 = 7 + 1
7 : 2 = 3 + 1
3 : 2 = 1 + 1
1 : 2 = 0 + 1
That means 123 = 1111011.

The presentation ends. Applause echoes through the ice cave. Chef Pebble smiles.

Chef Pebble: "Very nice. Now... can someone build a converter?"

Gini and Karl exchange a look.

Gini: "We already did."

🐧❄️

Welcome to the Ice Converter!

Type a frosty number below (binary like 1010 or decimal like 42):

references

https://www.rapidtables.com/convert/number/binary-to-decimal.html