A binary number is a number that consists of only 0 and 1. We use decimal numbers, which consist of numbers made up from 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The decimal system is also known as the denary system. Binary is critical to how computers operate, but that would take time to explain in detail. For your examples that you asked for, the following is how binary and decimal represent numbers from decimal 0 to decimal 10.
0 = 0
1 = 1
10 = 2
11 = 3
100 = 4
101 = 5
110 = 6
111 = 7
1000 = 8
1001 = 9
1010 = 10
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The binary code for eleven is 1011. 1011 = 23 + 21 + 20 = 8 + 2 + 1
As an editorial comment, there are only 10 types of people, those who understand binary and those who don't. For those who "don't", 10 (binary) = 2 (decimal)
The binary system is numeric system with a base of 2, using only the numerals 0 and 1, or two gravitationally connected stars or other celestial objects which orbit around their centre of mass.
binary and bomb Blitz; Blitzkreig; bazooka;
All numbers are read in order of most significant digit to least significant digit. Binary digits are read right to left the same way numbers increase from right to left (our system of base 10). Numbers do not increase the same way we read (left to right). This is the same way we add, multiply and subtract in math. We start from the numbers on the right and move left if you prefer to think of it that way. With our usual system of base 10 numbers, each digit starts from "ones", then "tens", "hundreds" and so on moving from right to left. The same is with binary except that binary is only base 2. A 1 in the first position = 2^0 = 1. A 1 in the second position = 2^1 = 2 where each "one" is added for the final value. See below for examples. Our base 10 system goes one more step by mulitplying each number as you go, expanding on the zeros and ones to zeros through nines: 5062 = 2*(10^0)+6*(10^1)+0*(10^2)+5*(10^3) = 5062 For a binary example, if there are 8 bits in a byte, we get the following possibilities: 00000000 = 0 00000001 = (2^0) = 1 00000010 = (2^1) = 2 00000011 = (2^0)+(2^1) = 3 and so on and so forth... 10101011 = (2^0)+(2^1) +(2^3)+(2^5)+(2^7) = 1+2+8+32+126 = 171 and finally 11111111 = the sum of 2^n where n stands for the numbers 0 -> 7 = (2^0)+(2^1) +(2^3)+(2^4)+(2^5)+(2^6)+(2^7)+(2^8) = 255