University:
Boston University
Course:
MET CS 201 | Introduction to Programming
Academic year:

2023
Views:

16

Pages:

9
Author:

Naomi Whitehead

Binary 00010 01001 01110 00001 10010 11001 00010 11001: 01011 01001 01101 00001 01110 01001 10011 10011 00001 01101 00101 00111 00001 01110 00001 01110 00100 10011 10101 01101 00001 What is Binary Code???? -Uses 0 and 1, starts with 2^0 -Also known as base-2 number system -Used in modern computers for things like logic gates -Computers code to and from Binary -Invented in 3rd Century BCE BEFORE COMPUTERS!!! -It's super cool! -You can add, subtract, multiply, and even divide in Binary! -If the Binary number starts with one, the number is negative, else, the number is positive "There are 10 people in this world, ones who understand Binary and ones who don't" Cool (or not so cool) Pictures :) Conversion Base 10 to Binary! Start with: 25 Binary is base two, so let's use powers of two: 2^4 (16) is the largest power of two that fits in 25, so we put a 1 in the 16s place. 1 Now we subtract 16 from 25: 25 - 16 = 9. So, do the same for 9: what's the largest power of two that fits in 9? 2^3 = 8. We put a one in the 2^3 place. 1 1 Conversion: Base 10 to Binary II 9-8=1 2^0 is one, so we put a one there. 1 1 1 Since we didn't use 2^2 or 2^1, we put zeros there. 1 1 0 0 1 Because 25 is a positive number, you need to place 0 before your answer. Therefore, 25 in binary is... 011001 0 1 1 0 0 1 Conversion Part II 0 1 1 Binary to Base 10! Start with 011001 Our Base 2 places: 0 0 1 Now, every time there is a one above a power of 2, do that operation. Every time there isn't, add zero! 0 x 2^5 = 0 1 x 2^4 =16 1 x 2^3 =8 0 x 2^2 = 0 0 x 2^1 = 0 1 x 2^0 =1 Finally, add all the products together. 16+8+1=25! (sound familiar?) How To Play NIM.... Objective: To have your opponent remove the last circle from the pyramid, but you can only remove circles from one row of choice at a time. Who wants to try? The Secret of NIM... Revealed! Binary is the key to NIM. Each row of circles can be represented in binary. To win, each column of binary needs to have an even number of ones. This situation is called a stable state. 001 010 011 100 101