Binary mathematics

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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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