chapter1(Binary_Systems)_2010

# chapter1(Binary_Systems)_2010 - Dept of Electrical...

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1 Logic Design Tatung University Dept. of Electrical Engineering Number system 1 2010/2/23 Logic Design 1 E1550: Logic Design Chapter 1 Logic Design Tatung University Dept. of Electrical Engineering Number system 2 2010/2/23 Logic Design 2 s We live in the digital age . s Digital systems are everywhere. digital telephones, digital TV, DVD, digital camera, digital computers Performs a variety of information-processing tasks Digital systems can represent and manipulate discrete elements of information represented internally in binary form. Why digital?

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2 Logic Design Tatung University Dept. of Electrical Engineering Number system 3 2010/2/23 Logic Design 3 Why digital? s Most digital devices are programmable . s Dramatic cost reduction in digital devices results from advances in IC technology. s Digital systems can be extremely reliable by using error- correcting codes. Logic Design Tatung University Dept. of Electrical Engineering Number system 4 2010/2/23 Logic Design 4 Binary Numbers
3 Logic Design Tatung University Dept. of Electrical Engineering Number system 5 2010/2/23 Logic Design 5 Decimal Number s Ex. 7392.6 = 7 × 1000+3 × 100+9 × 10+2 × 1+6 × 0.1 = 7 × 10 3 +3 × 10 2 +9 × 10 1 +2 × 10 0 +6 × 10 -1 s The decimal number system is of base , or radix 10 because r the coefficients are any of the 10 digits (0,1,2,…,9) r the coefficients are multiplied by powers of 10 s In general, base– r (radix– r ) numbers . 1 or , 0,1, , . 1 1 2 2 1 1 0 0 1 1 1 1 1 2 1 0 1 1 - = = + + + + + + + + + = - = - - + - + - - - - - - - - + - - - - r a r a r a r a r a r a r a r a r a r a a a a a a a a a i n m i i i m m m m n n n n m m n n K L L L L radix point Logic Design Tatung University Dept. of Electrical Engineering Number system 6 2010/2/23 Logic Design 6 Binary Numbers 7392 = 7 × 10 3 + 3 × 10 2 + 9 × 10 1 +2 × 10 0 (11010.11) 2 = 1×2 4 +1×2 3 +0×2 2 +1×2 1 +0×2 0 +1×2 -1 +1×2 -2 = (26.75) 10 (B65F) 16 = 11×16 3 +6×16 2 +5×16 1 +15 = (46687) 10 (A=10, B=11, C=12, D=13, E=14, F=15) m m m m n n n n m m n n r a r a r a r a r a r a r a r a a a a a a a a a - - + - + - - - - - - - - + - - - - + + + + + + + + + = 1 1 2 2 1 1 0 0 1 1 1 1 1 2 1 0 1 1 . L L L L

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4 Logic Design Tatung University Dept. of Electrical Engineering Number system 7 2010/2/23 Logic Design 7 Binary Numbers 2 10 = 1 Kilo 2 20 = 1 Mega 2 30 = 1 Giga 2 40 = 1 Tera Logic Design Tatung University Dept. of Electrical Engineering Number system 8 2010/2/23 Logic Design 8 Arithmetic Operations with Binary Numbers 110111 Product: 1011 0000 1011 000110 Difference: 1010100 Sum: 101 Multiplier: -100111 Subtrahend: +100111 Addend: 1011 Multiplicand: 101101 Minuend: 101101 Augend: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10
5 Logic Design Tatung University Dept. of Electrical Engineering Number system 9 2010/2/23 Logic Design 9 Numbers Base Conversions s Converting a number in base r to decimal: r Expand the number in a power series and adding all the terms s Converting a decimal number to a number in base

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## This note was uploaded on 01/01/2012 for the course ECON 101 taught by Professor Smith during the Spring '11 term at Allan Hancock College.

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chapter1(Binary_Systems)_2010 - Dept of Electrical...

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