EE101Lecture3

EE101Lecture3 - Lecture 3 Slides Signed Systems (Signed...

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© Mark Redekopp, All rights reserved Lecture 3 Slides Signed Systems (Signed Magnitude, 2‟s Complement) Digital Logic
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© Mark Redekopp, All rights reserved Decimal Code Review 518 10 = ( ) BCD 518 10 = ( ) XS3 518 10 = ( ) 84-2-1 (0111 0101 1000) BCD = ? 10 (0111 0101 1000) XS3 = ? 10 (0111 0101 1000) 84-2-1 = ? 10
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© Mark Redekopp, All rights reserved Decimal Code Review 518 10 = (0101 0001 1000) BCD 518 10 = (1000 0100 1011) XS3 518 10 = (1011 0111 1000) 84-2-1 (0111 0101 1000) BCD = 758 10 (0111 0101 1000) XS3 = 425 10 (0111 0101 1000) 84-2-1 = 138 10 Question: With 4-bits we can make 16 combinations. Which combinations are illegal (not possible) when using 84-2-1 Code? Excess-3?
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© Mark Redekopp, All rights reserved Binary Representation Systems Integer Systems – Unsigned Unsigned (Normal) binary – Signed • Signed Magnitude 2‟s complement 1’s complement* Excess-N* Floating Point – For very large and small (fractional) numbers Codes – Text ASCII / Unicode – Decimal Codes • Weighted Codes – BCD (Binary Coded Decimal) / (8421 Code) 2421 Code* – 84-2-1 Code Non-weighted Codes – Excess-3 * = Not covered in this class
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© Mark Redekopp, All rights reserved Interpreting Binary Strings • Given a string of 1‟s and 0‟s, you need to know the representation system being used, before you can understand the value of those 1‟s and 0‟s. • Information (value) = Bits + Context (System) 01000001 = ? 65 10 „A‟ ASCII 41 BCD Unsigned Binary system ASCII system BCD System
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© Mark Redekopp, All rights reserved ASCII Code • Used for representing text characters • Originally 7-bits but usually stored as 8-bits in a computer • Example: – printf(“Hello \ n”); – Each character is converted to ASCII equivalent • „H‟ = 0x48, „e‟ = 0x65, … • \n = newline character – CR = carriage return character (moves cursor to start of current line) – LF = line feed (moves cursor down a line)
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© Mark Redekopp, All rights reserved Binary Representation Systems Integer Systems – Unsigned Unsigned (Normal) binary – Signed • Signed Magnitude 2‟s complement 1’s complement* Excess-N* Floating Point – For very large and small (fractional) numbers Codes – Text ASCII / Unicode – Decimal Codes • Weighted Codes – BCD (Binary Coded Decimal) / (8421 Code) 2421 Code* – 84-2-1 Code Non-weighted Codes – Excess-3 * = Not covered in this class
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© Mark Redekopp, All rights reserved Unsigned and Signed • Normal (unsigned) binary can only represent positive numbers – All place values are positive • To represent negative numbers we must use a modified binary representation that takes into account sign (pos. or neg.) – We call these signed representations
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Signed Number Representation
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This note was uploaded on 11/08/2009 for the course EE 101 at USC.

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EE101Lecture3 - Lecture 3 Slides Signed Systems (Signed...

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