EE101Lecture13

EE101Lecture13 - Introduction to Digital Logic Lecture 13:...

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© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 13: Adders Overflow
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© Mark Redekopp, All rights reserved Addition Half Adders Addition is done in columns Inputs are the bit of X, Y Outputs are the Sum Bit and Carry-Out (C out ) Design a Half-Adder (HA) circuit that takes in X and Y and outputs S and C out 011 0 + 011 1 110 1 = X = Y 11 0 Half Adder X Y S C out C out Sum 0 1 1 0 X Y C out S 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0
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© Mark Redekopp, All rights reserved Addition Half Adders • We‟d like to use one adder circuit for each column of addition Problem: No place for Carry-out of last adder circuit Solution Redesign adder circuit to include an input for the carry 01 10 + 01 11 11 01 = X = Y 1 10 Half Adder X Y S C out 0 1 1 0 Half Adder X Y S C out 1 1 0 1
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© Mark Redekopp, All rights reserved Addition Full Adders Add a Carry-In input(C in ) New circuit is called a Full Adder (FA) 01 1 0 + 01 1 1 11 0 1 = X = Y 1 1 0 Full Adder X Y C in S C out C out C in 0 1 0 1 0 X Y C in C out S 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1
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© Mark Redekopp, All rights reserved Full Adder Logic S = X xor Y xor Cin Recall: XOR is defined as true when ODD number of inputs are true…exactly when the sum bit should be 1 Cout = XY + XCin + Ycin Carry when sum is 2 or more (i.e. when at least 2 inputs are 1) Circuit is just checking all combinations of 2 inputs
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© Mark Redekopp, All rights reserved Addition Full Adders Use 1 Full Adder for each column of addition 0110 + 0111 Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out
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© Mark Redekopp, All rights reserved Addition Full Adders Connect bits of top number to X inputs 0110 + 0111 Full Adder X Y C in S C out 0 Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out 1 1 0
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© Mark Redekopp, All rights reserved Addition Full Adders Connect bits of bottom number to Y inputs 0110 + 0111 = X = Y Full Adder X Y C in S C out 0 1 Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out 1 1 1 1 0 0
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© Mark Redekopp, All rights reserved Addition Full Adders Be sure to connect first C in to 0 0110 + 0111 = X = Y Full Adder X Y C in S C out 0 1 Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out 1 1 1 1 0 0 0
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© Mark Redekopp, All rights reserved Addition Full Adders Use 1 Full Adder for each column of addition 0110 + 0111 1101 = X = Y 01100 Full Adder X Y C in S C out 0 1 1 0 0 Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out 1 1 0 1 1 1 1 1 0 0 1 0
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© Mark Redekopp, All rights reserved Addition Full Adders Use 1 Full Adder for each column of addition 0110 + 0111 1101 = X = Y Adder X Y C in S C out 0 1 1 0 0 Full Adder X Y C in S C out Full Adder X Y C in S C out Full Adder X Y C in S C out 1 1 0 1 1 1 1 1 0 0 1 0 01100
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© Mark Redekopp, All rights reserved
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EE101Lecture13 - Introduction to Digital Logic Lecture 13:...

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