EE101Lecture14

EE101Lecture14 - Introduction to Digital Logic Lecture 14:...

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© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 14: Adders
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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 XY S C out C out Sum 01 1 0 1 0 0 0 C out 0 1 1 1 0 1 1 1 0 0 0 0 S Y X
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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 •P r o b l e m : – 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 XY S C out 01 1 0 Half Adder S C out 11 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 XY C in S C out C out C in 01 0 1 0 1 1 1 0 1 0 0 0 C out 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 S C in Y X
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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 XY C in S C out Full Adder C in S C out Full Adder C in S C out Full Adder 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 = X Full Adder XY C in S C out 0 Full Adder C in S C out Full Adder C in S C out Full Adder 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 XY C in S C out 0 1 Full Adder C in S C out Full Adder C in S C out Full Adder 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 XY C in S C out 0 1 Full Adder C in S C out Full Adder C in S C out Full Adder 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 XY C in S C out 0 1 1 0 0 Full Adder C in S C out Full Adder C in S C out Full Adder 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 Full Adder X Y C in S C out 0 1 1 0 0 Full Adder XY C in S C out Full Adder C in S C out Full Adder 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 Addition – Full Adders • Use 1 Full Adder for each column of addition 0110 + 0111 1101 = X = Y Full Adder XY C in S C out 0 1 1 0 0 Full Adder X Y C in S C out Full Adder C in S C out Full Adder 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 Addition – Full Adders
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EE101Lecture14 - Introduction to Digital Logic Lecture 14:...

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