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Binary Mathematics Counting system There are three kinds of people in the world: those who can count, and those who can not Wisdom - Unknown Today’s class Numbering system Conversion between 10 based and 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 = x 100 + x 10 + x = x 102 + x 101 + x 100 Binary Code Imagine a specie that only has two fingers how can they count? A computer is such kind of two-finger specie and Each place is the exponential of Base 10 vs Base Base 10 157 157 = x 100 + x 10 + x = x 102 + x 101 + x 100 Base 1011 = x 23 + x 22 + x 21 + x 20 1011 = x + x + x + x Binary Bits and Bytes bit is a single bit of information, a or Only two possible values byte is bits, an bit word 256 possible values from 0-255 base 10 or 00000000 to 11111111 base 10100110 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 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 Binary Hex Binary Hex 0000 1000 0001 1001 0010 1010 A 0011 1011 B 0100 1100 C 0101 1101 D 0110 1110 E 0111 1111 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 10100101 (Bin) Convert Decimal number to binary code 176 (Dec) Convert Hexadecimal number to binary BADDEF Add these two binary numbers 10001101+11011100=? Answer 10100101 (Binary) = 165 (Decimal) 176 (Decimal)= 10110000 (Binary) BADDEF=1011,1010,1101,1101,1110,1111 The result of summation 101101001 [...]...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 Binary Hex Binary Hex 0000 0 1000 8 0001 1 1001... the world, those who use binary counting system, and those who don’t Quiz No Calculators!!!! Convert binary code to Decimal number 10100101 (Bin) Convert Decimal number to binary code 176 (Dec) Convert Hexadecimal number to binary BADDEF Add these two binary numbers 10001101+11011100=? Answer 10100101 (Binary) = 165 (Decimal) 176 (Decimal)= 10110000 (Binary) BADDEF=1011,1010,1101,1101,1110,1111
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