Binary Numbers

So what are they and why are they important?

Decimal System vs. Binary System

• The Decimal System is a Base 10 system. That simply means it uses 10 symbols.

(0,1,2,3,4,5,6,7,8,9)

• The Binary System is a Base 2 system. It only uses 2 symbols. (0 and 1)

Binary in Computing Necessary for only 2 symbols because computers/ electronics

recognize only: “ON” (represented by 1) or “OFF” (represented by 0)

For computers, this 2 symbol system is crucial because it increases speed, memory and utilization

These binary digits (“0” and “1”) are known as “bits”

Understanding Binary

• In the decimal system, let’s take the number: 150 for example:

the “ones” column is represented by 0The “tens” column is represented by 5The “hundredths” column is represented by 1

As we go from right to left, the columns represent increasing powers of 10. Ones to tens, tens to hundredths, etc.

Understanding Binary• However, the Binary Number System, from

right to left increases in powers of 2.• (128, 64, 32, 16, 8, 4, 2, 1)

• So, since we can easily figure out the value of each column: we can deduce what the number is judging by whether there is a “1” (yes to that value) or “0” (none of that value) in that column.

Binary numbers

• Let’s take the binary number: 10

The column on the far right is the 1 column and the 0 indicates no value present.

The column on the left is the 2 column and the “1” means there is a value of 2 present.

So 10 in binary (remember this reads as 1 and 0, not

“ten”)= 2 in the decimal system.

Binary Numbers• Now’s let’s watch a brief video to better

understand how to convert the numbers from binary to decimal and vice versa.

Binary Numbers in 60 seconds: http://www.youtube.com/watch?v=qdFmSlFojIw&NR=1

Binary System Lesson Plan

References“Binary Numbers” image retrieved from http://atgfw.com/data.html.

Video retrieved on 9/18/2011 from: http://www.youtube.com/watch?v=qdFmSlFojIw&NR=1.

Website retrieved on 9/18/11 from: http://www.kerryr.net/pioneers/binary.htm.

Website retrieved on 9/19 from: http://homepage.ntlworld.com/interactive/.

Website retrieved on 9/19 from: http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary.

Website retrieved on 9/19 from: http://www.helpwithpcs.com/courses/binary-numbers.htm.

Website retrieved on 9/19 from: http://www.state.nj.us/education/cccs/standards/8/index.html.