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(Example)
F = A + B (C + D)
= A + B (CD)
Note that (CD) = C + D and (AX) = A + X
F = (A (B (CD)))
Now there is no OR operation in the Booleanexpression. Note that
A NAND B = (AB)
NAND-ONLY LOGIC CIRCUITS
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F= (A (B (CD)))
The logic circuit for this function is given by:
We can also use the same procedure to do NOR only gates.
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Ch2. Decoder
Dr. Bernard Chen Ph.D.
University of Central ArkansasSpring 2009
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Integrated Circuits An integrated circuit is a piece (also called
a chip) of silicon on which multiple gates or
transistors have been embedded
These silicon pieces are mounted on a plastic
or ceramic package with pins along the edgesthat can be soldered onto circuit boards orinserted into appropriate sockets
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Integrated Circuits
SSI, MSI, LSI:They perform small tasks such as addition offewbits. small memories, small processors
VLSITasks: - Large memory - Complex microprocessors, CPUs
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An SSI chip contains
independent NAND gates
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Examples of Combinational
Circuits a) Decoders
b) Encoders c) Multiplexers
d) Demultiplexers
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Decoder Accepts a value and decodes it
Output corresponds to value of n inputs
Consists of:
Inputs (n)
Outputs (2n , numbered from 0 p 2n - 1)
Selectors / Enable (active high or active low)
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The truth table of 2-to-4
Decoder
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2-to-4 Decoder
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2-to-4 Decoder
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The truth table of 3-to-8
DecoderA2 A1 A0 D0 D1 D2 D3 D4 D5 D6 D7
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
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3-to-8 Decoder
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2-to-4 Decoder: NAND
implementationDecoder is enabled when E=0 and an output is active if
it is 0
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Decoder Expansion Decoder expansion
Combine two or more small decoders with
enable inputs to form a larger decoder
3-to-8-line decoder constructed from two2-to-4-line decoders The MSB is connected to the enable inputs if A2=0, upper is enabled; if A2=1, lower is
enabled.
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Decoder Expansion
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Combining two 2-4 decoders to form
one 3-8 decoder using enable switch
The highest bit is used for the enables
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Combinational Circuit Design with
Decoders Combinational circuit implementation with
decoders
A decoder provide 2n minterms of n inputvariables
Since any Boolean function can beexpressed as a sum of minterms, one canuse a decoder and external OR gates toimplement any combinational function.
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Combinational Circuit Design with
Decoders
Example Realize F (X,Y,Z) = (1, 4, 7) with a decoder: