# Carnival of Space 10001110

By Phil Plait | February 24, 2010 2:10 pm

I have no idea why I converted the number of this week’s Carnival of Space into binary, except that I did a ternary conversion on Twitter recently and it was fun.

Yes, I’m a dork. But you laughed, so you are too.

CATEGORIZED UNDER: Astronomy, Space

1. Hold on… The previous Carnival post said it was #139, and 10001110 binary is 142. Did you miss two posts, or did you mess up the conversion?

(You may be a dork, but I’m a geek.)

2. QuietDesperation

Real men use hex.

3. Yeah, well, I quickly converted “10001110” to “8E” and went from there.

4. When I was, oh, I forget exactly but let’s say twelve, I wrote down the numbers from 1 to 100 in binary using noughts and crosses for zeroes and ones respectively. It is fun, isn’t it?

For the Binary Impaired, that’s also 0x8E. For the ancient gurus who struggled with the dinosaurs of the computing world it’s 0216.

6. Derek

ok guys, help me read this. The wiki explanation of binary numbers just has me DUMBfounded

Yup. There are 10 kinds of people: those who speak binary, and those who don’t!

And MadScientist: I also am one of the old-timers who can converse in octal – first learned by programming in octal on a DEC PDP-8.

8. Boo

I didn’t laugh, nerd.

but I do enjoy your blog, keep up the good work!

And MadScientist: I also am one of the old-timers who can converse in octal – first learned by programming in octal on a DEC PDP-8.

PDP-8? You should check out TWiT.tv’s Security Now! Steve Gibson, the host with Leo Laporte, has been buying up real and re-creations of PDP-8’s and is learning to program them. He’s also pretty good on security (as the program name indicates).

J/P=?

10. Motoman

There are 10 kinds of people in this world…
…those who can read binary, and those who can’t.

11. ScottDogg

You think you’re a dork? At my 31st birthday party I had a cake with 8 candles in a row on it — the right 5 were lit and the left 3 were unlit. Beat that!

12. jcm

10001110 = 0x8E = 0216

13. here

Here’s a question:

The colonization of space has been compared to the colonization of the New World. If we assume this analogy, where exactly are we in those terms?

Additionally, what would the New World look like when we got there?

It seems like we have only just learned how to make small boats, and sail around the coast, and the New World isn’t exactly fertile. In fact, it doesn’t even have soil to plant things in.

(I don’t really buy the analogy in the first place though….I don’t think the economics are similar enough to make it useful. I’m curious how others see it though).

There are II kinds of people in the world

Those who understand Roman Numerals, and those who don’t….

J/P=?

15. The Playboy Scientist

10001110 in binary is 142.

16. Jeffersonian

@derek
In binary, instead of having ten numerals to count with (0,1,2,3,4,5,6,7,9,), you only have two (0,1)
The first two are obvious: 0=zero and 1= 1.
But since there is no numeral for the value=2, you have to express “2” using the ones and zeros, so you express it as “10”
(because you have “start over” in the next column, just like you do when you get to “nine”, in the decimal system and you have to start over in the next column using a one and a zero for ten=10).
So, in binary, since two=10, then the way to represent the next value, three, is to add a “1” to the right column; three=11. And so forth.

@Derek #6: It’s easy – as Tom Lehrer might say, It’s just like the base 10 – if you only have 2 fingers (what he actually said was Base 8 is just like Base 10 if you’re missing 2 fingers).

So to quickly review the base 10, you have digits 0..9 (that’s 0 up to the base minus 1, since we’re talking base 10, that’s 9). Any positive integer (and zero) is represented as an implied sequence of sums of a digit multiplied by a power of your base. So 142 = 1*10^2 + 4*10^1 + 2*10^0 — aren’t you glad you only have to write 142? As already pointed out, the range of the digits is 0 up to one less than your base. So for the base 10 that’s 0..9, for base 8 it’s 0..7, for binary digits (base 2) it’s 0 and 1 only. Just to confuse things, hexadecimal (base 16) has the digits 0..F (the letters A .. F represent the numbers 10 .. 15).

So for a generic base X any number can be written exactly the same as we do for base 10 – except that you may need more or less symbols. Going back to that binary digit above: 1000 1110 this is:

1*2^7 + 0*2^6 + 0*2^5 + 0*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 0*2^0

or in decimal:

128 + 0 + 0 + 0 + 8 + 4 + 2 + 0 — which is 142.

18. complex field

Um… -14?

I also am one of the old-timers who can converse in octal – first learned by programming in octal on a DEC PDP-8.

Sure, but can you read ASCII punch tape?

20. Howard H

@19: What memories… my 12th birthday present a Synertek 6502 single-board kit – with a KSR-35 teletype for an RS-232 terminal, with the full punch & reader combo.

Verifying program entries via the hex membrane keyboard by dumping memory to the serial port, with the KSR switched to tape output only, then scanning the tape punches by eye, muttering to myself “MOV, MOV, ADD, STOre, …”

The good old days

21. rdpayne

My fingers still remember how to load the switch register in hex.

Oh, yeah, that was how the boot program got into memory. After that you hit run (A switch on the computer front panel) and load some actual software into core memory from the paper tape in the teletype.

22. Derek

@MadScientist & Jeffersonian….Thanks for the explanation. I had to read both a few times but I think i get it. But just a few questions: In binary language, the base will always be ‘2’?

So if i see a number written in binary, this binary sequence will always have to be 8 digits? And the base will always be 2? Or if I see a binary sequence with only 4 digits I will know the base will be 2, but the first digit will be 3, next 2, next 1, final 0?

So no matter what, the last digit will always be 0?

23. Gamercow

Ah, Binary. The best way to be able to count to over 500 on your fingers.

24. Gamercow

@derek: The best way I’ve seen it introduced to people is to think of it the same way you learned base 10 numbers. In base 10, a number can be broken out to “places”, i.e 1’s column, 10’s,100’s, 1000’s, etc. In base 2, its 1’s, 2’s, 4’s, 8’s, 16’s, 32’s, etc.

So, if 8367 in base 10 is 7 1’s + 6 10’s + 3 100’s +8 1000’s, or 7(1) + 6(10) + 3(100) + 8(1000),

then 100101 would be 1(1) + 0(2) + 1(4) + 0(8) + 0(16) + 1(32). Soon enough, you’ll be ignoring the 0s, and thinking of it as 1(1)+1(4)+1(32) or 37.

Lastly, a binary number is odd if it ends in 1, even if it ends in 0.

25. Jeffersonian

@derek
Eight digits just means the data is an 8-bit string, or is a binary number requiring eight columns to be represented. The last digit (column) can be “1” or “0”, just like any other column.

My description was how to create numbers in binary, MAd Science was explaining how to read binary numerals. Let my try to explain this way:

You are accustomed to the decimal system, which has ten available numerals available to represent numbers (0,1,2,3,4,5,6,7,8,9). In decimal, zero is represented by the numeral “0”, one by “1”, two=2, three=3, nine=9, etc. But once you get past nine, you have to use two of those numerals to represent the amount “ten”, because you’ve run out of numerals. You do this by adding a second column, and starting over; that is, you write “10” for ten. I.E. you have to use two columns, in decimal, to represent the amount “ten”.

Because chips are semiconducting, they can only make either/or decisions. Therefore, they use the binary system instead of decimal. In binary, there are only two available numerals to represent amounts, instead of nine. Those two are: “1” and “0”.

For the first two numbers in binary, it’s the same as in decimal: 0 = zero and 1= one. But then you run out of numerals before you can represent two (just like you ran out after nine, in decimal), so you have to add a new column. So, in binary we represent “two” by starting a new column and using the numerals that are available. Thus, two is represented in binary by writing “10”.

Hence the joke “there are only 10 (two) kinds of people in the world”.

To represent the next amount, in sequence (three), you then add the next numeral to the right column (because you haven’t “used” it yet in the two column config). I.E., three is represented by “11”.
four=100
five=101
And so on, adding columns as you need. For example, to represent “ten” in binary, since you can only use “1” and “0” as numerals, you need to have four columns: “1010”.

26. Jeffersonian

Another way to look at it is to “reverse engineer” the process.

If you had to represent the numbers one through twenty, but could only use the numerals “1” and “0” to represent those numbers, how would you do it?

27. Jeffersonian

“In binary, there are only two available numerals to represent amounts, instead of nine.”
should be:
“In binary, there are only two available numerals to represent amounts, instead of ten.”

(sorry derek, one typo can really confuse things!)

@MadScientist 17 – thank you! I actually understand how to decode it now!
Up until this point I could not for the life of me figure it out (I think the people explaining it to me were just trying too hard)

29. Gamercow:

Ah, Binary. The best way to be able to count to over 500 on your fingers.

I can count to 1,023. Are you missing a finger?

They’re also a great hex/octal/binary converter.

Of course, given BA’s recent foray into ternary, you can count to 59,048 if you’re up to the challenge.

And he still hasn’t commented on whether he missed two Carnivals, or messed up his binary conversion.

30. Oh, if you want to really confuse people who have trouble with bases other than decimal, you can point out that everything is written in base 10 when written in the base you are talking about.

ie:

Two in binary is “10”.
Three in ternary is “10”.
Eight in octal is “10”.
Ten in decimal is “10”.
Thirty-seven in base thirty-seven is “10”.

NEW ON DISCOVER
OPEN
CITIZEN SCIENCE