Incrementing and Decrementing 91509 L 15 Decoders Multiplexers

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Incrementing and Decrementing 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De.

Incrementing and Decrementing 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 1

Class 18 a – Special arithmetic circ. o Incrementers Decrementers Circuits o Material from

Class 18 a – Special arithmetic circ. o Incrementers Decrementers Circuits o Material from section 4 -5 of text o o 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 2

Incrementer o o o Often just want to increment the value by 1 and

Incrementer o o o 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: n n SUM = A xor B xor Cin Cout = AB + ACin + BCin 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 3

Incrementer o o Often we just want a circuit to create the value +1

Incrementer o o 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 n Sum = A Å B Å Cin n Cout = AB + BCin + ACin Now if B = 0 these reduce to n n o Inc. Sum = A Å Cin Inc Carry= A 0 + B 0 + ACin = ACin A Half Adder!!! 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 4

Implementation o A increment unit o Note that hardware can be simplified if you

Implementation o A increment unit o Note that hardware can be simplified if you have a unit that always increments. 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 5

A Decrementer o Want to subtract 1 from the input. reduces to o o

A Decrementer o Want to subtract 1 from the input. reduces to o o What are the equations n n n Difference D=AÅBÅBorin reduces to AÅBorin Borrow-out Bout= BBorin + A’B+A’Borin Reduces to Bout = A’Borin 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 6

The circuit o And again can do a dedicated circuit o And again can

The circuit o And again can do a dedicated circuit o And again can do a multiple bit implementation with simplification of the lsb and msb. 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 7

Class 18 a assignment o o Covered sections 4 -5 Problems for hand in

Class 18 a assignment o o Covered sections 4 -5 Problems for hand in n o Problems for practice n o none Reading for next class: sections 5 -1, 5 -2 9/15/09 - L 15 Decoders, Multiplexers Copyright 2009 - Joanne De. Groat, ECE, OSU 8

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