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Lecture+13

# Base2isanumbersystemlike base2isanumbersystemlike

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Unformatted text preview: we are acting on? Data Representation Data Representation All data inside the computer is represented by bits. Bits can have only two values 0 or 1. 4 bits make a nibble 8 bits make a byte 11001010 10101011 Data Encoding Data Encoding Bytes 11001110 10101010 11110000 10100101 11111111 11001110 11001110 Meaning Hail! to the victors valiant Hail! Hail! Each bit allows two possibilities. 1 bit: 0 1 (2 things) 2 bits: 00 01 10 11 (4 things) 3 bits: 000 001 010 011 100 101 110 111 (8 things) n bits: 2n things 8 bits: 256 things How many things can you encode How many things can you encode with a byte (8 bits)? Base 2 is a number system like Base 2 is a number system like base 10 456,347 Base 2 is a number system like Base 2 is a number system like base 10 456,347 100000 105 4 10000 104 5 1000 103 6 100 102 3 10 101 4 1 100 7 Base 2 is a number system like Base 2 is a number system like base 10 456,347 100000 105 4 10000 104 5 1000 103 6 100 102 3 10 101 4 1 100 7 4 x 105 + 5 x 104 + 6 x 103 + 3 x 102 + 4 x 101 + 7 x 100 Base 2 is a number system like Base 2 is a number system like base 10 110001 32 25 1 16 24 1 8 23 0 4 22 0 2 21 0 1 20 1 1 x 25 + 1 x 24 + 0 x 23 + 0 x 22 + 0 x 21 + 1 x 20 Base 2 is a number system like Base 2 is a number system like base 10 110001 32 25 1 16 24 1 8 23 0 4 22 0 2 21 0 1 20 1 1 x 25 + 1 x 24 + 0 x 23 + 0 x 22 + 0 x 21 + 1 x 20 110001(base 2) = 32+16+1 = 49(base 10) 128 27 Convert the Binary Number to Convert the Binary Number to Decimal 64 26 32 25 16 24 8 23 4 22 2 21 1 20 01011001 1- 27 2- 89 3- 67 4- 79 128 27 Convert the Binary Number to Convert the...
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