BinaryBinary

A double zero educational presentation

Binary Basics

• Binary is the language computers use

• Only 1’s and 0’s can be found in Binary

• Very large numbers can be translated into Binary.

Binary Digit System

• Non Binary• 1’s 10’s 100’s 1,000’s 10,000’s 100,000’s 1,000,000’s

• Binary

• 1’s 2’s 4’s 8’s 16’s 32’s 64’s 128’s

Steps to convert a number to Binary

• Chose a number below 255

• For this example, we will choosing 176

Step One

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• Is 176 bigger than 128?

• Yes, so place a one in the 128’s place

• Then subtract 128 from 176.

• The result is 48

Step Two

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• 1_____________________________

• Is 48 bigger than 64?

• No, place a zero under the 64’s place

Step Three

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• 1_____0________________________

• Is 48 greater than 32?

• Yes, subtract 32 from 48.

• The result is 16

Step Four

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• 1_____0___1____________________

• Is 16 equal to or greater than 16?

• Yes, subtract 16 from 16.

• The result is zero.

Step Five

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• 1_____0___1____1_______________

• Due to the fact that zero is less than all remaining digits place zeros in all remaining digits.

Step Six

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• 1_____0___1____1__0___0__0___0_

• So the number 176 would be 1011000 in binary, represented by a byte of 8 bits.

• 128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

• 1_____1___1____1__1___1__1___1_

• If all the bits in the byte were 1’s, which would be its highest value, it would add up to 128 + 64 + 32 + 16 + 8 +4 + 2 + 1= 255.

• The highest value a byte can have is 255.