Binary: Counting with 1s and 0s

1. Binary: Counting with 1s and 0s Data BSU CS4MS 4/9/19 http://www.cs.bsu.edu/cs4ms/docs/BinarySlides.pptx

2. Exponents review Exponents show a number multiplied by itself a certain number of times. 2x is the same as 2 times itself x times. It is read as “2 to the x power”. Examples: 22 is the same as 2x2 45 is the same as 4x4x4x4x4 21 is the same as 2 Note: Any number to the 0th power is equal to 1.

3. What is Binary? Binary is just a different way to count numbers but only using 1s and 0s. Usually you count up to 1, 2, 3, 4, … ,8, 9 and when you reach 9, you go to 10 which is adding a new placeholder. There is a ones spot and a tens spot. _1_ 10 _0_ 1 For Binary, you can only use 1s and 0s so when you get to 1, you have to add a new placeholder and put in a zero. So it starts at 0 = 0, then 1 = 1. Instead of using 2, we can only use 1s and 0s. So 2 = 10. Then 3 = 11 and 4 = 100. _1_ 2 _0_ 1

4. More Binary 8 + 0 + 2 + 1 = 11 1011 in binary is equal to 11 in decimal All numbers greater than or equal to zero.

5. Examples 0111 in binary = (0 x 23) + (1 x 22) +( 1 x 21) + (1x 20) = 0 + 4 + 2 + 1 = 7 1011 1111 in binary = (1 x 27) + (0 x 26) + (1 x 25) + (1 x 24) + (1 x 23) + (1x 22) + (1 x 21) + (1 x 20) = 128 + 0 + 32 + 16 + 8 + 4 + 2 + 1 = 187

6. Binary Helpful example about teaching binary: https://www.exploringbinary.com/how-i-taught-third-graders-binary-numbers/ Useful activities for teaching binary: https://classic.csunplugged.org/wp-content/uploads/2014/12/unplugged-01-binary_numbers.pdf