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."