Chapter  start   Previous  page  Next  page

2.4.4   Exclusive-OR Cell

The two-input exclusive-OR ( XOR , EXOR, not-equivalence, ring-OR) function is

  A1   A2 = XOR(A1, A2) = A1 · A2' + A1' · A2.(2.32)

We are now using multiletter symbols, but there should be no doubt that A1' means anything other than NOT(A1). We can implement a two-input XOR using a MUX and an inverter as follows (2 gates):

  XOR(A1, A2) = MUX[NOT(A1), A1, A2],(2.33)


  MUX(A, B, S) = A · S + B · S '.(2.34)

This implementation only buffers one input and does not buffer the MUX output. We can use inverter buffers (3.5 gates total) or an inverting MUX so that the XOR cell does not have any external connections to source/drain diffusions as follows (3 gates total):

  XOR(A1, A2) = NOT[MUX(NOT[NOT(A1)], NOT(A1), A2)].(2.35)

We can also implement a two-input XOR using an AOI21 (and a NOR cell), since

  XOR(A1, A2) = A1 · A2' + A1' · A2 = [ (A1 · A2) + (A1 + A2)' ]'

  = AOI21[A1, A2, NOR(A1, A2)],(2.36)

(2.5 gates). Similarly we can implement an exclusive-NOR (XNOR, equivalence) logic cell using an inverting MUX (and two inverters, total 3.5 gates) or an OAI21 logic cell (and a NAND cell, total 2.5 gates) as follows (using the MUX function of Eq. 2.34):

  XNOR(A1, A2) = A1 · A2 + NOT(A1) · NOT(A2)

  = NOT[NOT[MUX(A1, NOT (A1), A2]]

  = OAI21[A1, A2, NAND(A1, A2)](2.37)

Chapter  start   Previous  page  Next  page

Teledyne Optech
GEOINT2017 - Countless CAD add-ons, plug-ins and more.

Internet Business Systems © 2017 Internet Business Systems, Inc.
595 Millich Dr., Suite 216, Campbell, CA 95008
+1 (408)-337-6870 — Contact Us, or visit our other sites:
AECCafe - Architectural Design and Engineering EDACafe - Electronic Design Automation TechJobsCafe - Technical Jobs and Resumes  MCADCafe - Mechanical Design and Engineering ShareCG - Share Computer Graphic (CG) Animation, 3D Art and 3D Models
  Privacy Policy