Lecture_13

# Lecture_13 - ECE 331 Digital System Design Multi-bit Adder...

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ECE 331 – Digital System Design Multi-bit Adder Circuits (Lecture #13)

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Ripple Carry Adder 1 0 1 0 1 0 0 1 + 1 Carry-in 0 1 0 0 1 Carry-out 1 1 Carry ripples from one column to the next
FA x n – 1 c n c n 1 y n 1 s n 1 FA x 1 c 2 y 1 s 1 FA c 1 x 0 y 0 s 0 c 0 MSB position LSB position Ripple Carry Adder Carry ripples from one stage to the next Carry-in Carry-out

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Ripple Carry Adder n-bit Ripple Carry Adder - Composed of n 1-bit Full Adders - Carries ripple from LSB stage to MSB stage Delay ~ (n)*(delay of single FA stage) Area required is linear in n 4-bit Ripple Carry Adder - Composed of 4 1-bit Full Adders
The Ripple Carry Adder is slow . How can the speed of the adder be increased?

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Increasing the speed of the Adder Method A: Include all inputs and outputs in the design - Inputs = X i , Y i , C in,i ; Outputs = S i , C out,i 1-bit 3 inputs 2 outputs 2-bit 5 inputs 3 outputs 4-bit 9 inputs 5 outputs n-bit 2n+1 inputs n+1 outputs - Large number of operands, but only 2 logic levels Increase in speed Increase in area required decrease propagation delay increase # of logic gates Use Truth Table and K-Map to derive logic functions
Increasing the speed of the Adder Method B: Manipulate the Boolean Algebra

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