Incrementing and Decrementing

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Presentation transcript:

Incrementing and Decrementing 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Class 18a – Special arithmetic circ. Incrementers Decrementers Circuits Material from section 4-5of text 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Copyright 2009 - Joanne DeGroat, ECE, OSU Incrementer Often just want to increment the value by 1 and that is the only operation needed. An incrementer is a circuit that is much simpler than an adder. Start with the equations: SUM = A xor B xor Cin Cout = AB + ACin + BCin 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Copyright 2009 - Joanne DeGroat, ECE, OSU Incrementer Often we just want a circuit to create the value +1 each time. The circuit is a significant simplification. Start with the equations for general addition Sum = A Å B Å Cin Cout = AB + BCin + ACin Now if B = 0 these reduce to IncSum = A Å Cin Inc Carry= A0 + B0 + ACin = ACin A Half Adder!!! 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Copyright 2009 - Joanne DeGroat, ECE, OSU Implementation A increment unit Note that hardware can be simplified if you have a unit that always increments. 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Copyright 2009 - Joanne DeGroat, ECE, OSU A Decrementer Want to subtract 1 from the input. reduces to What are the equations Difference D=AÅBÅBorin reduces to AÅBorin Borrow-out Bout= BBorin + A’B+A’Borin Reduces to Bout = A’Borin 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Copyright 2009 - Joanne DeGroat, ECE, OSU The circuit And again can do a dedicated circuit And again can do a multiple bit implementation with simplification of the lsb and msb. 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU

Copyright 2009 - Joanne DeGroat, ECE, OSU Class 18a assignment Covered sections 4-5 Problems for hand in none Problems for practice Reading for next class: sections 5-1, 5-2 9/15/09 - L15 Decoders, Multiplexers Copyright 2009 - Joanne DeGroat, ECE, OSU