9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU1 Decoders and...

9/15/09 - L15 Decoders, Multiplexers

Copyright 2009 - Joanne DeGroat, ECE, OSU 1

Decoders and Multiplexer Circuits



Class 17 – Arithmetic Functions Iterative Combinational Circuits Binary Adders

Material from section 4-1 and 4-2 of text

Iterative Circuits The concept – Create a functional block and

create the circuit for doing the multiple bit operation by simply repeating it.

Another concept to be introduced – circuit contraction where you fix the value of some inputs and then can simplify the resulting circuit. Examples are incrementing, decrementing or multiplying by a constant.



Iterative Circuit Consider an iterative circuit that operates on

two binary vectors. Base unit

Iterative connection.



Iterative circuit area A lot in arithmetic area of application.

Adders Subtractors Incrementors Decrementors Multiplication circuits



Binary Adders Consider adding 2 binary digits. Can specify the requirement in a truth table.

A combinational circuit that adds two input bits is called a half adder.



Half adder equations The Sum and Carry equations

Implementation



S = X’Y + XY’ = X Y

C = XY

The full adder Can evolve half adder into a full adder. Full adder truth table and minimization.



S=X’Y’Z+X’YZ’+XY’Z’+XYZ = X Y Z = (X Y) Z

The full adder continued The carry minimization

Implementation



C = XY +XY’Z +X’YZ = XY +Z(XY’+X’Y) = XY + Z(X Y)

The full adder Have just seen a full adder implemented from the

structural connection of two half adders and an OR gate.

Can do a direct implementation. It will end up with the same number and type of gates.

For a multibit implementation need a symbol for the unit.



Multibit use And then can use that symbol in multibit or

hierarchical representations. A 2 bit example

In this adder the final output carry is generated in the final stage after the carry inputs to all the previous stages has settled.



Carry ripple So the carry ripples from the lsb to msb A

ripple carry adder.

All inputs, As,Bs, and C0 arrive – C1 becomes valid – C2 becomes valid – C3 becomes valid – C4 becomes valid -



Class 17 assignment Covered sections 4-1 through 4-2 Problems for hand in

none Problems for practice

4-2

Reading for next class: sections 4-3, 4-4



9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU1 Decoders and...

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