How to convert numbers from numerical numbers to binary.?

Question

Please explain

Answer 1

Binary is nothing more than powers of two. For example, the number 37 in decimal is 3 * 10 + 7. In binary, it would be 100101, which is 1 * 2^5 + 1 * 2^2 + 1, or 32 + 4 + 1. To convert a number to binary, you need to divide it by two, and then arrange the consecutive remainders in reverse order. Let's take 37 again:

37 / 2 = 18 r 1
18 / 2 = 9 r 0
9 / 2 = 4 r 1
4 / 2 = 2 r 0
2 / 2 = 1 r 0
1 / 2 = 0 r 1

And there you have our binary number once more: 100101 (the remainders in reverse order).

Good luck.

Answer 2

You create the binary number one digit at a time, from right to left.
Here's how:

1. Divide the "regular" number (the base 10 number) by 2. If it was an odd number, there will be a remainder of 1, and the first binary digit that you write down is a 1. If it was an even number, there is no remainder and you write down 0. This is the rightmost digit of the binary number.

2. Take the number that you got when you divided by 2, and divide by 2 again. If the remainder is 1, put a 1 to the left of the first digit. If the remainder is 0, put a 0 to the left of the first digit.

3. Divide by 2 again, and put the remainder at the left end of the binary number that you are creating.

4, 5, 6, ... etc. Continue with the same process until the division results in an answer of 0 with a remainder of 1, where the 1 is the leftmost digit of the binary number.

Example: Convert 74 to a binary number.

74 / 2 = 37 with a remainder of 0
Binary digits (so far): 0

37 / 2 = 18 with a remainder of 1
Binary digits (so far): 10

18 / 2 = 9 with a remainder of 0
Binary digits (so far): 010

9 / 2 = 4 with a remainder of 1
Binary digits (so far): 1010

4 / 2 = 2 with a remainder of 0
Binary digits (so far): 01010

2 / 2 = 1 with a remainder of 0
Binary digits (so far): 001010

1 / 2 = 0 with a remainder of 1
Binary digits (so far): 1001010

And that brings us down to 0, so the final answer
(74 expressed in binary) is 1001010.

If you have decimal places (a number like 74.23), then you need a further process to handle the .23 part. If you want to know about that, ask another question.

Answer 3

binary numbers are powers of two just like decimal numbers are powers of ten. each place represents an increasing power of two as you move away from the decimal point. (Binary point. - heh)

What this means is we can get any number by adding up powers of two (incuding 1 = 2^0 ).
the powers of 2 are 1,2,4,8,16,32,64,etc.
Any number can be turned into the following formula
N=a*1+b*2+c*4+d*8+e*16+f*32+g*64+etc. where a,b,c,d,e,f,g, etc. are either 0's or 1's and the sequence "...gfedcba" is the binary number representation of N.
examples 1=1, 2=10, 32=100000, 34=100010.
you can add binary numbers just like decimal except you have to "carry one" a lot more. for each place you have only four possibilities 0+0, 1+0, 0+1, or 1+1. the sums are 0,1,1,10 repspectively. Using long addition and remembering to carry to the next place will get you the right answer

Converting Decimal to Binary

Easiest way is to find a calculator that does the calculation automatically. Many scientific calulators do. Some computer software will do this also.
But, assuming you're doing it by hand:
1. I assume that negative numbers can be represented by the minus sign just like negative decimal numbers. Most computers do NOT use this format, but rather a complement format which I will not go into here.
1.1 Remove the minus sign, if present.
2. Separate the whole number from the fraction (if the number has both) I will not cover fractions here. They are treated ALMOST the same.
3. For the whole number you need to find the largest power of 2 that is less than the whole number.

Make a table of powers of two. 1,2,4,8,16,32,... on the left and their binary representation on the right 1,10,100,1000,10000,...

If you don't know how to add binary numbers then this will just be totally confusing. Sorry.

4. Subtract the largest power of two that is less than the number from the number and add the powers binary representation

example: 303 so the biggest power of two that is less than 303 is 256 = 2^8.
subtract 256 from 303 and put down 100000000 to start with (getting it from the table)

the remainder is 47 so 32 is the largest power of 2 less than 47
subtract 32 from 47 and add 100000 to the above
100000000 + 100000 = 10010000 (you got 100000 from the table, right?)

remainder is 15 and 8 is the largest power of 2 8= 1000
10011000 and 7

7 -> 100 & 3
3 -> 010 & 1 (I added the 0 on the far left to help adding)
1 -> 001 and we're done!
so we have 303 = 10101111

hopefully you don't need to do fractions as they are a little bit more complicated!

Answer 4

The usual ('numerical numbers') way of counting is in decimal ('dec' stands for ten, where as 'bi' from binary means two).

Binary is just like using a number system which, instead of being based around the number 10, is based around the number 2.

When we count using our number system, we count 0-9 and then add 1 to the number on the left to keep our place, and then start back at 0

If you want to count in binary, there would be only two symbols you'd be allowed to use - 0 and 1 instead of 0-9.
So you would count like this:
0 (0), 1 (1), 00 (2), 01 (3), 11 (4), 000 (5), 001 (6), 011 (7), 111 (8)
etc.
(I hope this makes sense)

Junk:
Old civilisations used to use number systems based around the number 6.
With 10 symbols to use (in a decimal system) - 0-9, if we only had space for 8 digits/symbols, we could count 10,000,000 numbers (10^8). Where as, if we could only use a maximum of 8 symbols in binary, we could only count 2^8 numbers (or 256).
This number is used a lot in computers which have '8 bits to a byte' because if a byte is a letter and a bit is '0 or 1', the computer can describe 256 letters if they divide each letter into 8 bits. Computers use binary because '1' represents 1 electrical pulse and '0' represents a space of no pulses. (I'm going off topic).

Answer 5

Another good way to find the binary value of a number is to divide it by two, note the remainder, and divide the result until you get zero. The remainders give you the binary value. Here is an example of what I mean.

Lets say you want to find the binary value of 45

46/2 = 23 remainder 0
23/2 = 11 remainder 1
11/2 = 5 remainder 1
5/2 = 2 remainder 1
2/2 = 1 remainder 0
1/2 = 0 remainder 1

So the binary value of 46 is 101110.

Answer 6

Take the largest power of 2 that does not exceed the number and subtract it from the number. Then, take the next largest power of 2 that does not exceed the remainder and subtract that. Repeat this process until the remainder is zero. An example will help


137 - 128 (which is 2^7) = 9
9 - 8 (which is 2^3) = 1
1 - 1 (which is 2^0) = 0

1 0 0 0 1 0 0 1

Notice how I filled in the powers of two that could not be subtracted with zeros.

Answer 7

Binary is base 2.

Reading from right to left, the first bit (1 or 0 value) represents 1, the second 2, the third 4, the fourth 8, and so on and so forth.

For example, to represent 42, you would write

0010 1010

Answer 8

The binary numeral system (base 2 numerals) represents numeric values using two symbols, typically 0 and 1. More specifically, binary is a positional notation with a radix of two. Owing to its relatively straightforward implementation in electronic circuitry, the binary system is used internally by virtually all modern computers.

see more detail at
http://en.wikipedia.org/wiki/Binary_numeral_system

Answer 9

This Site Might Help You.

RE:
How to convert numbers from numerical numbers to binary.?
Please explain

Answer 10

z o r r o has a good scheme, but what you're actually doing is converting numbers from base ten to base two. All numbers of whatever base are "numerical".........