Does anyone know how to operate binary numbers off the top of their head?

Question

if I wrote 11111111, would you know what number it represented immediately? Is it necessary to remember it in this way? What will be the benefits?

Answer 1

After a lot of years of dealing with binary numbers, you do tend to develop some skill with them. For example, I instantly recognized your number as one less than 1 0000 0000, which is 2^8, which is 256, so your number is 255. It helps to group them 4 digits at a chunk (actually called a nibble), that way each chunk represents a power of 16, and as you work with them for awhile, you'll tend to notice and memorize things like:

1nibble - 16 states/numbers
2 nibbles - 256 states/numbers
3 nibbles - 4096 states/numbers
4 nibbles - 65,536 states/numbers
Every power of 2 up to 65536, maybe higher
Every 10 binary digits is a power of 1024, ie,
2^10 = 1k
2^20 = 1M
2^30 = 1G
2^40 = 1T

Things like that. It's not entirely necessary to memorize, but you won't be able to help it if you spend much time with them. The benefit? Just convenience.

Answer 2

actually addition is not too hard
similar to digital numbers, you have a carry-on

example: 101+111
..................abc abc

(c) 1+1=0, a carry-on 1
(b) 1+0 =1 add carry-on from (a) 1+1 = 0, a carry-on 1
(a) 1+1=0 a carry-on 1, add the carry-on from (b)

The result: 1100
indeed: 101= 5, 111=7, 11+5 = 12 which is 1100 in base 2


"if I wrote 11111111"
in this case yes because:
1+2^1+2^2+...+2^n = 2^(n+1)-1
Hence 11111111 = 2^9-1 = 612-1=611

I know the powers of 2 up tp 2^11=2048,

"What will be the benefits?"
Well, I don't see the benefits. Let the computer do its crunching numbers job.
In the movie "Pi", a gifted mathematician tries to find hidden connections while he watches binary sequences.

Answer 3

As another answerer already says, many computer programmers represent binary numbers in "hexadecimal" where there are sixteen possible digits (0 to 9, and A to F), each different digit representing 4 binary positions, or "bits". If you do this a lot, you get a feel for the size of these numbers, and also you can add and subtract them directly without converting them to decimal. I remember even once working a long division in hexadecimal, it was something like 2B4A80 divided by 17E, but I got the hex quotient and hex remainder far quicker than if I had converted everything to decimal and back again. My workmates could hardly believe it...

No, I don't think there's any need for this, or benefit from it.

Answer 4

No, just make the table for conversion, like with a colum for 2 to the power of 0, then 2 to the power of 1, then 2 to the power of 2, etc, 11111111 would be

Answer 5

Generally there isn't much need to be that fast at converting from binary to decimal. Typically in systems where you are actually using binary all your inputs and outputs will be in binary and it doesn't matter what the values are in decimal and vice versa.

Often in computers hexidecimal is used instead of binary, because then you can read it more quickly and naturaly. hexidecimal used 0-9 and a-f to represent binary values of 0000 to 1111. So 4 binary digits are represented with 1 alphanumeric, or 8 "bits" can be represented with 2 "hex"

Certainly, being able to convert quickly will never hurt you, and could benefit you by making you faster at it than most of your peers.

Answer 6

yes 255, computer registries are an on off system thus it is comprised of 1 and 0 ons and offs so to calculate you use just these 1 and 0 also 255 is the largest number 8 bit registries can store.

Answer 7

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