Binary Number System A Binary Number is made up of only 0s and 1s. This is 1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8) (=13.625 in Decimal) Similar to the Decimal System, numbers can be placed to the left or right of the point, to indicate values greater than one or less than one. For Binary Numbers: The number just to the left of the point is a whole number, we call this place units. As we move left, every number place gets 2 times bigger. The first digit on the right of the point means halves (1/2). As we move further right, every number place gets 2 times smaller (one half as big). 2 Different Values Because you can only have 0s or 1s, this is how you count using Binary: Decimal: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Binary: 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 "Binary is as easy as 1, 10, 11." Here are some more equivalent values: Decimal: 20 25 30 40 50 100 200 500 Binary: 10100 11001 11110 101000 110010 1100100 11001000 111110100 Definition of Binary The word binary comes from "Bi-" meaning two. We see "bi-" in words such as "bicycle" (two wheels) or "binocular" (two eyes). When you say a binary number, pronounce each digit (example, the binary number "101" is spoken as "one zero one", or sometimes "one-oh-one"). This way people don't get confused with the decimal number. Bits A single binary digit (like "0" or "1") is called a "bit". For example 11010 is five bits long. The word bit is made up from the words "binary digit" How to Show that a Number is Binary To show that a number is a binary number, follow it with a little 2 like this: 1012 This way people won't think it is the decimal number "101" (one hundred and one). Examples Example 1: What is 11112 in Decimal? The "1" on the left is in the "2×2×2" position, so that means 1×2×2×2 (=8) The next "1" is in the "2×2" position, so that means 1×2×2 (=4) The next "1" is in the "2" position, so that means 1×2 (=2) The last "1" is in the units position, so that means 1 Answer: 1111 = 8+4+2+1 = 15 in Decimal Example 2: What is 10012 in Decimal? The "1" on the left is in the "2×2×2" position, so that means 1×2×2×2 (=8) The "0" is in the "2×2" position, so that means 0×2×2 (=0) The next "0" is in the "2" position, so that means 0×2 (=0) The last "1" is in the units position, so that means 1 Answer: 1001 = 8+0+0+1 = 9 in Decimal   Example 3: What is 1.12 in Decimal? The "1" on the left side is in the units position, so that means 1. The 1 on the right side is in the "halves" position, so that means 1×(1/2) So, 1.1 is "1 and 1 half" = 1.5 in Decimal Example 4: What is 10.112 in Decimal? The "1" is in the "2" position, so that means 1×2 (=2) The "0" is in the units position, so that means 0 The "1" on the right of the point is in the "halves" position, so that means 1×(1/2) The last "1" on the right side is in the "quarters" position, so that means 1×(1/4) So, 10.11 is 2+0+1/2+1/4 = 2.75 in Decimal "There are 10 kinds of people in the world, those who understand binary numbers, and those who don't."