l2combintl_logic

# L2combintl_logic - L2 Combinational Logic Design(Construction and Boolean Algebra Acknowledgements Materials in this lecture are courtesy of the

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L2: 6.111 Spring 2004 1 Introductory Digital Systems Laboratory L2: Combinational Logic Design L2: Combinational Logic Design (Construction and Boolean Algebra) (Construction and Boolean Algebra) Acknowledgements: Materials in this lecture are courtesy of the following people and used with permission. - Randy H. Katz (University of California, Berkeley, Department of Electrical Engineering & Computer Science) - Gaetano Borriello (University of Washington, Department of Computer Science & Engineering, http://www.cs.washington.edu/370) - Rabaey, A. Chandrakasan, B. Nikolic. Digital Integrated Circuits: A Design Perspective . Prentice Hall, 2003.

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L2: 6.111 Spring 2004 2 Introductory Digital Systems Laboratory The Inverter The Inverter Truth Table IN OUT 01 10 IN OUT "1" "0" V OH V IH V IL V OL Undefined Region V(x) V IH V IL Slope = -1 Slope = -1 V OL V OH V(y) V OH NM L = V IL -V OL NM H = V OH -V IH V OL ± Large noise margins protect against various noise sources
L2: 6.111 Spring 2004 4 Introductory Digital Systems Laboratory MOS Technology: The NMOS Switch MOS Technology: The NMOS Switch D G S gate N+ P-substrate N+ drain source V T = 1V V s R NMOS R NMOS Switch Model OFF ON V GS < V T V GS > V T NMOS ON when Switch Input is High

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L2: 6.111 Spring 2004 5 Introductory Digital Systems Laboratory PMOS: The Complementary Switch PMOS: The Complementary Switch S G D gate P+ N-substrate P+ drain source V T = -1V V s R PMOS R PMOS OFF Switch Model ON V GS > V T V GS < V T PMOS ON when Switch Input is Low
L2: 6.111 Spring 2004 6 Introductory Digital Systems Laboratory The CMOS Inverter The CMOS Inverter IN OUT V DD V DD Switch Model S R PMOS G G OUT R NMOS IN IN D D S Rail-to-rail Swing in CMOS

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L2: 6.111 Spring 2004 7 Introductory Digital Systems Laboratory Possible Function of Two Inputs Possible Function of Two Inputs X Y F X Y 16 possible functions (F 0 –F 15 ) 0 00000000011111111 0 10000111100001111 1 00011001100110011 1 10101010101010101 X Y X NOR Y NOT (X OR Y) X NAND Y NOT (X AND Y) 1 0 NOT X X AND Y X OR Y NOT Y X XOR Y X = Y There are 16 possible functions of 2 input variables: In general, there are 2 (2^n) functions of n inputs
L2: 6.111 Spring 2004 8 Introductory Digital Systems Laboratory Common Logic Gates Common Logic Gates Gate Symbol Truth-Table Expression XY Z 0 0 1 1 01 11 10 X Y Z NAND Z = X • Y 0 0 1 1 00 X Y AND Z Z = X • Y 0 0 1 1 Z X Y Z = X + Y NOR 0 0 1 1 Z X Y OR Z = X + Y

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L2: 6.111 Spring 2004 9 Introductory Digital Systems Laboratory Exclusive (N)OR Gate Exclusive (N)OR Gate XY Z 0 0 1 1 00 11 01 10 Z = X Y + X Y X or Y but not both ("inequality", "difference") X Y Z XOR (X Y) 0 0 1 1 XNOR (X Y) Z = X Y + X Y X and Y the same ("equality") Z X Y Widely used in arithmetic structures such as adders and multipliers
L2: 6.111 Spring 2004 10 Introductory Digital Systems Laboratory Generic CMOS Recipe Generic CMOS Recipe V dd A 1 F(A 1 ,…,A n ) pullup : make this connection when we want F(A 1 ,…,A n ) = 1 pulldown : make this connection when we want F(A 1 ,…,A n ) = 0 A n ...

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## This note was uploaded on 07/21/2009 for the course EECS 6.111 taught by Professor Prof.ananthachandrakasan during the Spring '04 term at MIT.

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L2combintl_logic - L2 Combinational Logic Design(Construction and Boolean Algebra Acknowledgements Materials in this lecture are courtesy of the

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