Can someone simply explain how to undestand the binary system??

Answer 1

The binary system is a number system based on 2 rather
than 10. All binary numbers are expressed as a string of
1's and 0's.

In the familiar ten-based number system, the places of
the digits indicate a multiple of some power of ten.

1 = 1x10^0
10 = 1x10^1 plus 0x10^0
11 = 1x10^1 plus 1x10^0
21 = 2x10^1 plus 1x10^0
213 = 2x10^2 plus 1x10^1 plus 3x10^0

From right to left each place is a multiple of the next
highest power of 10 beginning with 10^0 at the right.

The binary system uses 2 as its base which means that
each digit from right to left represents a multiple of the
next highest power of 2 beginning with 2^0 on the right.

When you count in the 10-based system you use the
digits 0-9.

When you count in the binary(2-based) system you
use only the digits 0 and 1.

In the binary system the number 1111 means:
1x2^3 plus 1x2^2 plus 1x2^1 plus 1x2^0 which is 8 plus 4
plus 2 plus 1 or 15.

When counting in the binary system, the first ten numbers
are 01, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010 which
corresponds to 1, 2 , 3, 4, 5, 6, 7, 8, 9, 10 in the common 10-based number system.

Take the binary number 1000000. start with 2^0 for the
rightmost digit, can you see that this means 1x2^6 or 64?

How about 1000100? Can you see that this means
1x2^6 plus 1x2^2 or 68?

Now look at 1000101? Can you see that this means
1x2^6 plus 1x2^2 plus 1x2^0 or 69?

101...Can you see that this is 1x2^2 plus 1x2^0 or 5?

111...1x2^2 plus 1x2^1 plus 1x2^0 or 7?

Answer 2

Any system to represent numbers is based on powers. Our everyday "decimal" system values each position as a power of 10.

In the number 3612, the values are (beginning at the right side:
2 x 1 = 2
1 x 10 = 10
6 x 100 = 600
3 x 1000 = 3000
Total = 3612.
The base of the decimal system is 10.

In the binary system, the base is 2.
A number such as 110101 is (again, from the right)
1 x 1 = 1
0 x 2 = 0
1 x 4 = 4
0 x 8 = 0
1 x 16 = 16
1 x 32 = 32

Total (when written in the decimal system): 53

The rules for adding and multiplying are the same.

In a decimal sum, if two numbers of the same "rank" total more than 10, you "carry over" the ten(s) and keep the units.

For example 57 + 26
the 7 and the 6 add up to 13. You keep the 3 in the same position and "carry over" the 1 to the next column where 5+2 becomes 5+2+1 = 8
Sum = 83 (and not "seventy-thirteen")

Except that in binary, it is when the sum reaches 2 that you carry-over:
Using the same number (57+26)

111001 + 011010 =
units: 1 + 0 = 1
twos: 0 + 1 = 1
fours: 0 + 0 = 0
8's : 1 + 1 = 0 (carry 1 to next level)
16's: 1+1+1 = 1 (carry 1 to next level)
32's: 1 + 0 + 1 = 0 (carry 1 to next level)
64's: 0 + 0 + 1 = 1

Sum = 1010011 in binary.

Answer 3

Binary numbers are made up of 1's and 0's. It works the same way as the decimal system, except that you use "2" instead of "10"

375 in decimal is 3 * 100 + 7 * 10 + 5

10010 in binary is the same as

1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2 + 0 =
1 * 16 + 1 * 2 = 18 in decimal.

If you have any more questions about this, please feel free to e-mail me. I've worked with decimal, octal, hexadecimal, etc. for a very long time.

Answer 4

Binary is a base two system represented with 1 and 0;
Our decimal system is base 10, represented with numbers 0-9.
In binary, you simply use 1 and 0; to count, use the following pattern:
0
1
10
11
100
101
110
111
1000
... and so on.
Also, the computer reads everything in 1 and 0; 1=on, 0=off

Answer 5

Binary system uses only two number; 0 & 1
so, compared with the decimal system:
0 = 0
1 = 1
10 = 2
11 = 3
100 = 4
101 = 5
110 = 6
111 = 7
1000 = 8
1001 = 9
1010 = 10
and so on

Its adventage (used on computers mainly) is that by having only two numbers, one means right, and the other one means wrong. No way to get lost in a ramifyed system.

Answer 6

in decimal, a 4 digit number abcd means
a x 10^3 + b x 10^2 + c x 10^1 + d x 10^0
= 1000a + 100b + 10c + d

similarly abcdef means
100000a + 10000b + 1000c + 100d + 10e + f

In binary system,
abcd means a x 2^3 + b x2^2 + c x 2^1 + d x2^0
= 8a + 4b + 2c + d
similarly abcdef means
32a + 16b + 8c + 4d + 2e + f