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# week1 - Week 1 Introduction to Computing and the 8051...

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1 Week 1 Introduction to Computing and the 8051 Microcontrollers Chapters 0 and 1

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2 110.101 b = 6.625 6A.C = 106.75 10 = 1010 b 10 = 12 8 0.125 = 0.001 b 0.78125 = 0.C8 h Binary and Hexadecimal Systems Conversion to decimal: 110.101 b = ? 6A.C h = ? Conversion from decimal for a whole number: divide by the radix and save the remainder as the significant digits 10 = ? B 10 = ? 8 Converting from a decimal fraction multiply the decimal fraction by the radix save the whole number part of the result repeat above until fractional part of step 2 is 0 0.125 = ? b 0.78125 = ? h
3 Base 16 Number systems Represent 100111110101b in hex Group them 1001 1111 0101 9 F 5 hex Convert 1714d to binary 1714 = 16*107 +2 107 = 16*6 + 11 1714 = 6B2 h = 0110 1011 0010 b

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4 Signed Representation-Two’s Complement If the number is positive make no changes If the number is negative, complement all bits and add by 1 -6 => 0000 0110 + 1 = 1111 1001 + 1 = FAh 8 bit signed numbers 0 to 7Fh (+127) are positive numbers 80h (-128)to FFh (-1) are negative numbers Conversion of signed binary numbers to their decimal equivalent 1101 0001 1101 0001 + 1 = 0010 1110 + 1 = 0010 1111 = 2Fh => -47 1000 1111 0101 1101 (16 bit signed number) 0111 0000 1010 0010 + 1 = 0111 0000 1010 0011 = 70C3h => -28835 Two’s complement arithmetic +14 - 20 0000 1110 + 0001 0100 + 1 = FAh Overflow: Whenever two signed numbers are added or subtracted the possibility exists that the result may be too large for the number of bits allocated Ex: +64 +96 using 8-bit signed numbers
5 Two’s complement Numbers in the range from -2 7 to 2 7 -1 are represented by 8 bit signed arithmetic 7Fh 0111 1111b +127 01h 0000 0001b 1 00h 0000 0000b 0 FFh 1111 1111b -1 FEh 1111 1110b -2 82h 1000 0010b -126 81h 1000 0001b -127 80h 1000 0000 b -128 Hex Binary Decimal

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6 ASCII The standard for text In this code each letter of the alphabet, punctuation mark, and decimal number is assigned a unique 7-bit code number With 7 bits, 128 unique symbols can be coded Often a zero is placed in the most significant bit position to make it an 8-bit code e.g., Uppercase A 41h Digits 0 through 9 are represented by ASCII codes 30h to 39h
7 ASCII - more

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8 BCD BCD code provides a way for decimal numbers to be encoded in binary form that is easily converted back to decimal 26 (unsigned binary)=> 1Ah = 0001 1010 b 26 (BCD)=>26h=0010 0110 b 243 (unsigned binary)=> F3h= 1111 0011 b 243 (BCD)=>243h=> 0010 0100 0011 b Unpacked BCD: One byte to store each digit 243 (Unpacked BCD)=> 02 04 03h =>00000010 00000100 00000011 b
9 Digital Primer Inversion

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10 AND and OR Gates
11 XOR Gate

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12 Logic Design using Gates Two implementations of a half-adder

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15 Multiplexer

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16 N to 2 N Decoder

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18 Latch The simplest memory element Level-sensitive : it memorizes the input data when there is a given level on the control input
19 D type flip flop (DFF) The only Flip-Flop we use (forget SR, JK, etc.) The most used memory element Edge-sensitive : it memorizes the input data when there is a specific transition (e.g., 0 Æ 1) on the control input

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20 DFF with Enable If EN = 0 when there is an edge, the edge is ignored; If EN = 1, normal behaviour
21 Registers

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22 Tri-state Buffers Transistor circuit for inverting tri-state buffer: “high impedance” (output disconnected) Variations Tri-state “transmission gate” Inverting buffer Inverted enable
23 Tri-state Buffers

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week1 - Week 1 Introduction to Computing and the 8051...

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