The World of ones and zeros By: Priyanka, Emily, and Trisha

What is it? A system in which information can be expressed by combinations of the digits 0 and 1 You use it everyday and you don’t know it A base 2 number system This is a table of the first few numerals in the system:

Who used it Natives of a remote Polynesian island Western mathematicians Electronic devices We used it to make this wonderful PRESENTATION!!!!!!!!!!!!!!!!!!!!!!!

Traveling Back in time The Natives of a remote Polynesian island and Ancient Greeks may have invented a binary number system, similar to the one used by computers to calculate, centuries before Western mathematicians did Later, Gottfried Wilhelm Leibniz, invented a binary numeral system and showed that it could be used in a primitive calculating machine(computers) Leibniz invented his version in the seventeenth century It is not known who had invented it first, Leibniz or the Natives

Why use it Natives of a remote Polynesian island may have used it to keep track of the trading network Today, it forms the backbone of all modern computing systems

Binary vs. decimal SIMILARITIES BINARY DECIMAL Uses only ones (1) and zeroes (0) Base 2 Does not use the same place value Addition: 1+2(Decimal)=1+10(Binary)=11 - They both use ones and zeroes They both are number systems They both have whole parts fractional parts They both use place value Uses 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 Base 10 Does not use the same place value Addition: 1+2=3

Steps to add in binary 1. Align the numbers you wish to add as you would if you were adding in decimal numbers(remember that only numbers with ones and zeroes are applicable). 2. Start with the two numbers in the far right column. 3. Add the numbers following the rules of decimal addition, unless both numbers are a one. 4. Add 1+1 as 10 if present. 5. Start on the next column to the left hand side. 6. Repeat the steps above, but add any carry. Ex. 101 +111 -------------

Steps to subtract in this system 1. Align the numbers as an ordinary subtraction problem(remember to only use ones and zeros) 2. Borrow from the second digit if you need to regroup 3. Solve the right most column first 4. Finish the problem Ex. 1101 - 10 ---------------------

Steps to Multiply in binary form Just align the digits properly(remember to only use ones and zeros) Multiply like decimal system Ex. 101 x 10 --------------------

Bye – Bye-nary