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ECE 2020 - 29 Feb - 4 Mar Lecture Notes

by: Connor Hawley

ECE 2020 - 29 Feb - 4 Mar Lecture Notes ECE 2020 A

Connor Hawley

GPA 4.0
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About this Document

On Interpreting the titles: For lecture notes: L means lecture M means Monday, T means Tuesday, W means Wednesday, R means Thursday, and F means Friday. For book notes: Ch. means chapter Sc. means ...
Digital System Design
Dr. Joseph L. Hughes
Class Notes
intro, Digital, Design, ECE, 2020




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This 5 page Class Notes was uploaded by Connor Hawley on Sunday March 6, 2016. The Class Notes belongs to ECE 2020 A at Georgia Institute of Technology - Main Campus taught by Dr. Joseph L. Hughes in Winter 2016. Since its upload, it has received 16 views. For similar materials see Digital System Design in Electrical Engineering at Georgia Institute of Technology - Main Campus.


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Date Created: 03/06/16
L: M Monday, February 29, 2016 12:06 PM Other codes - 01011110could be: ○ 94 unsigned integer ○ Some character ○ Invalid binary coded decimal ○ Symbol - ASCII ○ Defined as a 7-bit protocolwith 128 symbols ○ There were some special characters for formatting text ○ Also, 8-bit computersprocessed these in their 7-bit forms with an 8 appended to the front - Takeaway - know these things exist Signed numbers - Fixed-point - N bits - 2^n patterns ○ 2^n values - Split them (roughly) evenly - Deal with zero Simplest format - Sign-magnitude ○ A one bit sign followed by an n - 1 bit magnitude - Range of this format ○ ○ +- zero ○ -1 - Issues ○ Rules for addition and subtraction will depend on if signed bits are same or different ○ Plus or minus zero is a pain Complementedformats - 1's complement ○ ○ Negative value - complementall bits ○ ○ Turns out this is going to have arithmetic challenges - 2's complement ○ ○ Negative value - complementthe bits and add 1 ○ ○ Addition and subtraction work L: W Wednesday, March 2, 2016 12:02 PM - Four bit chart for bit representation(thank god) - 6-bit 2's C ○ Range: -32 - 31 - Example ○ ○ ○ This refers to overflow - result is greater than the number system can represent ○ Overflowcan be checked using XOR to compare the carry in and carry out - To subtract, just add negative numbers ○ Also, using the extra negative bit in arithmeticof 2's complementis going to be very difficult ○ Because there's no positive2^n - Just look at how pretty this is - L: F Friday, March 4, 2016 11:57 AM - HA (half adder) ○ Inputs - 2 bits ○ Outputs - 2 bits  Sum 2^0  Carry 2^1 - FA (full adder) ○ Inputs - 3 inputs  2 data bits  1 carry bit ○ Output - 2 bits  Sum  Carry - N-bit adder (ripple carry) - However,the "ripple" in this calculation moves very slowly ○ It is more efficient to separate the full adders and carry using a mux - Use carry look-ahead ○ If you add the carry-out, you can quickly correct output - Adder-subtractor - You can do multiplication without iterative addition: use indexed addition


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