COMPUTER E
COE 308 - BINARY NUMBERS

# COE 308 - BINARY NUMBERS - 8 inches(20 cm in diameter Die...

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8 inches (20 cm) in diameter Die area is 250 mm 2 About 16 mm per side 55 million transistors per die 0.18 μm technology Size of smallest transistor Improved technology  uses 0.13 μm and 0.09 μm Dies per wafer = 169 When y ield = 100% Number is reduced after testing Rounded dies at boundary  are useless Different Representations of Natural Numbers XXVII Roman numerals (not positional)27 Radix-10 or decimal number (positional) 11011 2 Radix-2 or binary  number (also positional) Fixed-radix positional representation with k digits Number N in radix r = ( d k 1 d k –2 . . . d 1 d 0 ) r Value=d k –1 × r k –1 +d k –2 × r k –2 +...+d 1 × r +d 0 Examples: (11011) 2 = 1×2 4 + 1×2 3 + 0×2 2 + 1×2 + 1 = 27 (2103)

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Unformatted text preview: (2103) 4 =2×4 3 +1×4 2 +0×4+3=147 Each binary digit (called bit) is either 1 or 0 Bits have no inherent meaning, can represent Unsigned and signed integers CharactersFloating-point numbers Images, sound, etc. Bit NumberingLeast significant bit (LSB) is rightmost (bit 0)Most significant bit (MSB) is leftmost (bit 7 in an 8-bit number) Each bit represents a power of 2Every binary number is a sum of powers of 2 DecimalValue=( d n-1 ×2 n-1 )+. ..+( d 1 ×2 1 )+( d 0 ×2 ) Binary(10011101) 2 =2 7 +2 4 +2 3 +2 2 +1=157 Repeatedly divide the decimal integer by 2Each remainder is a binary digit in the translated value...
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• Fall '08
• MuhamedMudawar
• Numerical digit, Positional notation, Decimal, Numeral system, diameter Die area, XXVII Roman numerals

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