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Chapter_1_Digital_Systems_and_Binary_Numbers

# Chapter_1_Digital_Systems_and_Binary_Numbers -...

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Digital Logic Design Ch1-1 Chapter 1 Digital Systems and Binary Numbers Mustafa Kemal Uyguroğlu Digital Logic Design I

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Digital Logic Design Ch1-2 Outline of Chapter 1 1.1 Digital Systems i 1.2 Binary Numbers i 1.3 Number-base Conversions i 1.4 Octal and Hexadecimal Numbers i 1.5 Complements i 1.6 Signed Binary Numbers i 1.7 Binary Codes i 1.8 Binary Storage and Registers i 1.9 Binary Logic
Digital Logic Design Ch1-3 Digital Systems and Binary Numbers Digital age and information age i Digital computers General purposes Many scientific, industrial and commercial applications i Digital systems Telephone switching exchanges Digital camera Electronic calculators, PDA's Digital TV i Discrete information-processing systems Manipulate discrete elements of information For example, {1, 2, 3, …} and {A, B, C, …}…

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Digital Logic Design Ch1-4 Analog and Digital Signal Analog system The physical quantities or signals may vary continuously over a specified range. i Digital system The physical quantities or signals can assume only discrete values. Greater accuracy t X(t) t X(t) Analog signal Digital signal
Digital Logic Design Ch1-5 Binary Digital Signal An information variable represented by physical quantity. i For digital systems, the variable takes on discrete values. Two level, or binary values are the most prevalent values. i Binary values are represented abstractly by: Digits 0 and 1 Words (symbols) False (F) and True (T) Words (symbols) Low (L) and High (H) And words On and Off i Binary values are represented by values or ranges of values of physical quantities. t V(t) Binary digital signal Logic 1 Logic 0 undefine

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Digital Logic Design Ch1-6 Decimal Number System Base (also called radix) = 10 10 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } i Digit Position Integer & fraction i Digit Weight Weight = ( Base) Position a Magnitude Sum of “ Digit x Weight a Formal Notation 1 0 -1 2 -2 5 1 2 7 4 10 1 0.1 100 0.01 500 10 2 0.7 0.04 d 2 *B 2 + d 1 *B 1 + d 0 *B 0 + d -1 *B -1 + d - 2 *B -2 ( 512 . 74 ) 1 0
Digital Logic Design Ch1-7 Octal Number System Base = 8 8 digits { 0, 1, 2, 3, 4, 5, 6, 7 } i Weights Weight = ( Base) Position a Magnitude Sum of “ Digit x Weight a Formal Notation 1 0 -1 2 -2 8 1 1/8 64 1/64 5 1 2 7 4 5 *8 2 + 1 *8 1 + 2 *8 0 + 7 *8 -1 + 4 *8 -2 =(330.9375) 10 ( 512 . 74 ) 8

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Digital Logic Design Ch1-8 Binary Number System Base = 2 2 digits { 0, 1 }, called b inary dig its or “ bits i Weights Weight = ( Base) Position a Magnitude Sum of “ Bit x Weight a Formal Notation i Groups of bits 4 bits = Nibble 8 bits = Byte 1 0 -1 2 -2 2 1 1/2 4 1/4 1 0 1 0 1 1 *2 2 + 0 *2 1 + 1 *2 0 + 0 *2 -1 + 1 *2 -2 =(5.25) 10 ( 101 . 01 ) 2 1 0 1 1 1 1 0 0 0 1 0 1
Digital Logic Design Ch1-9 Hexadecimal Number System Base = 16 16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F } i Weights Weight = ( Base) Position a Magnitude Sum of “ Digit x Weight a Formal Notation 1 0 -1 2 -2 16 1 1/16 256 1/256 1 E 5 7 A 1 *16 2 + 14 *16 1 + 5 *16 0 + 7 *16 -1 + 10 *16 -2 =(485.4765625) 10 ( 1E5 . 7A ) 16

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Digital Logic Design Ch1-10 The Power of 2 n n Mega Giga Tera Kilo
Digital Logic Design Ch1-11 Addition Decimal Addition 5 5 5 5 + 0 1 1 = Ten Base Subtract a Base 1 1 Carry

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Chapter_1_Digital_Systems_and_Binary_Numbers -...

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