ECE 4110– Sequential Logic Design

1. ECE 4110– Sequential Logic Design Lecture #19 • Agenda • MSI: Ripple Carry Adders • Announcements • HW# 9 assigned.

2. Ripple Carry Adder • Addition – Half Adder- one bit addition can be accomplished with an XOR gate (modulo sum 2) 0 1 0 1 +0+0+1+1 0 1 1 10- notice that we need to also generate a “Carry Out” bit- the “Carry Out” bit can be generated using an AND gate- this type of circuit is called a “Half Adder”- it is only “Half” because it doesn’t consider a “Carry In” bit

3. Ripple Carry Adder • Addition – Full Adder- to create a full adder, we need to include the “Carry In” in the SumCin A BCoutSum 0 0 0 0 0 0 0 1 0 1 Sum = A  B  Cin 0 1 0 0 1 Cout = Cin∙A + A∙B + Cin∙B 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- you could also use two "Half Adders" to accomplish the same thing

4. Ripple Carry Adder • Addition – Ripple Carry Adder- cascading Full Adders together will allow the Cout’s to propagate (or Ripple) through the circuit- this configuration is called a Ripple Carry Adder

5. Ripple Carry Adder • Addition – Ripple Carry Adder- What is the delay through the Full Adder? - Each Full Adder has the following logic: Sum = A  B  Cin Cout = Cin∙A + A∙B + Cin∙B - tFull-Adder will be the longest combinational logic delay path in the adder

6. Ripple Carry Adder • Addition – Ripple Carry Adder- What is the delay through the entire iterative circuit? - Each Full Adder has the following logic: tRCA = n·tFull-Adder- the delay increases linearly with the number of bits - different topologies within the full-adder to reduce delay (Δt) will have a n·Δt effect