Can any tell me the binary form of 2007...and can you explain to me how to do it?

Question

Its for extra credit. also I want to know how to do 2/1/90 in binary form, tomorrows my birthday and I just wanted to show my teacher lol.

Answer 1

Binary is just a series of powers of 2, just like decimal is a series of powers of 10 (2007 = 2 * 10^3 + 0 * 10^2 + 0 * 10^1 + 7 * 10^0)
First, find the largest power of two that's less than the number you want; in this case, it's 1024 = 2^10. So you'll need places for 2^10 down to 2^0.
10000000000 = 1024 in binary

adding 2^9 (512) gives 1540 which is still less than 2007, so you're good.
11000000000 = 1540

adding 256 gives 1796, so you're still good, etc, etc
Eventually, you'll arrive at 2007 = 11111010111. If you're lazy, though, you can just go into the Windows calculator, enter 2007, then click the () Bin button P:

Answer 2

Number systems are rather simple. We use the decimal system, or base 10, so a number like 569 is actually:

5*10^2 + 6*10^1 + 9*10^0
500 + 60 + 9
569


Binary is the same way... except you use a base of 2 instead of 10. So a number like 1011 is:

1*2^3 + 0*2^2 + 1*2^1 + 1*2^0
8 + 0 + 2 + 1
11

So, to figure out how to convert 2007 to binary, we need to work it backwards so to speak. We know 2007 is greater than 1024 (or 2^10) but less than 2048 (or 2^11), so we know it will be 11 binary digits.

1??????????

Now we move one digit to the right (2^9 or 512). We started with 2007, and now we've represented 1024, so we need to represent (2007-1024 = 983). Is 983 greater than 512? It is, so we know the next digit is a 1:

11?????????

Now we move to 2^8, or 256. We have left 983-512 = 471. Since 471 is greater than 256, again we have a 1:

111????????

Continue on... 2^7 = 128. 471 - 256 = 215. 215 > 128, so it's a 1:

1111???????

2^6 = 64. 215 - 128 = 87, 87 > 64, so another 1:

11111??????

2^5 = 32, 87-64 = 23. 23 is less than 32, so we have our first 0!

111110?????

2^4 = 16, 23 is greater than 16, so we have a 1 here:

1111101????

2^3 = 8, 23-16 = 7. 8 is greater than 7, so we have a 0:

11111010???

2^2 = 4, 7 is greater than 4, so another 1:

111110101??

2^1 = 2, 7-4 = 3, 3>2, so a 1:

1111101011?

2^0 = 1, 3-2 = 1, so we know the last digit is a 1:

11111010111

there is your answer!

To check it, you work it in reverse:

1*2^10 + 1*2^9 + 1*2^8 + 1*2^7 + 1*2^6 + 0*2^5 + 1*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 1024 + 512 + 256 + 128 + 64 + 0 + 16 + 0 + 4 + 2 + 1 = 2007!

I hope this makes sense and helps you understand the process! :)

Answer 3

Binary is expressing numbers in a 2 base rather than the ten base we normally use.

So, 3 in binary is 11. (Which is 2+1)
7 is 111 (4+2+1)
it can be determined by the right most digit is 2 raised to the power 0 and is included if it is 1. the second digit to the right is 2 to the power 1 and so on.

2007 is 2^10 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 2^2 + 2^1 + 2^0
so it is 11111010111.

I'm not sure how you want to express your birthday. Do you mean 10/1/11111000110?

Answer 4

11111010111

10/1/11111000110 = 2/1/1990