Binary Mathematics

Counting system There are three kinds of people in the world: those who can count, and those who can not. - Unknown Wisdom Today’s class Numbering system Conversion between 10 based and 2 based numbering system. Binary Mathematics. Quiz

Base 10 counting system We happened to use the current counting system, because we happened to have ten fingers. If dinosaurs had ruled the earth, they would be happy to use a 8-based counting system.

Numbers Ancient Africa Notches on a bone. Egyptians/Roman Each magnitude is represented by a symbol. Indian/Arabian (Modern numbering system) 1,475,268

Base 10 (Decimal numbers) What does 157 mean? 157 = 1 x x x 1 = 1 x x x 10 0

Binary Code Imagine a specie that only has two fingers. how can they count? A computer is such kind of two-finger specie. 0 and 1 Each place is the exponential of 2

Base 10 vs Base 2 Base = 1 x x x 1 = 1 x x x 10 0 Base = 1 x x x x = 1 x x x x 1

Binary Bits and Bytes 1 bit is a single bit of information, a 1 or 0 Only two possible values 1 byte is 8 bits, an 8 bit word 256 possible values from base 10 or to base is a single byte

Base 10 to Binary

Binary mathematics 0+0=0 1+0=1 1+1=10

Hexadecimal (base 16) Binary code is too long in representation. Hex is much shorter. Converting a binary number to a Hex number is relatively easy Every 4 bit can convert to a Hex Problem: we are short of numbers A-10 B-11 C-12 D-13 E-14 F-15

Lookup table BinaryHexBinaryHex A B C D E F

Example

Wisdom said There are 10 kinds of people in the world, those who use binary counting system, and those who don’t.

Quiz No Calculators!!!! Convert binary code to Decimal number (Bin) Convert Decimal number to binary code 176 (Dec) Convert Hexadecimal number to binary BADDEF Add these two binary numbers =?

Answer (Binary) = 165 (Decimal) 176 (Decimal)= (Binary) BADDEF=1011,1010,1101,1101,1110,1111 The result of summation