8.28 Binary & Representation Of Numbers

Whatarethenumerals base2 base3 base10 01 012

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Unformatted text preview: 2 1 1101 8 + 4 + 1 = 13 16 8 21 1 + 2 + 8 + 16 = 27 2 + 4 + 8 = 14 There are 10 kinds of people in the world: ­Those who know binary ­Those who do not Other Bases Base 3: 2012 = 2 x 33 + 0 x 32 + 1 x 31 + 2 x 30 = 2 x 27 + 0 x 9 + 1 x 3 + 2 x 1 = 54 + 0 + 3 + 2 = 59 Other Bases Base 16…. what are the numerals ? Base 2: Base 3: Base 10: {0,1} {0,1,2} {0,1,2,3,4,5,6,7,8,9} Base 16: {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F} 1CF = = 1 x 162 + 12 x 161 + 15 x 160 = 256 + 192 + 15 = 463 Word Size 8 bits = 11111111 = 255 16 bits = 1111111111111111 = 2^16 – 1 Binary and Hexadecimal Binary and Hexadecimal 0 0000 1 0001 8 1000 9 1001 How do we write 463 in Binary? 463=256 + 128 + 64 + 8 + 4 + 2 + 1 463 = 111001111 2 0010 A (10) 1010 3 0011 B (11) 1011 C (12) 1100 (Group the above by 4) 5 0101 D (13) 1101 6 0110 E (14) 1110 7 0111 F (15) 1111 4 0100 463 = 1 1100 1111 463 = 1 C F in Hex and vice­versa: 2EA = 0010 1110 1010 Binary Addition Decimal Addition Binary Addition 8423 6915 ­­­­­­­­­­ 1101011 1001101 ­­­­­­­­­­­ see http://www.youtube.com/w...
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