Combinational Circuit Arithmetic Circuit

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Combinational Circuit Arithmetic Circuit

• Parallel Adder
• Example 4-bit adder

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Combinational Circuit Arithmetic Circuit

• Cascading Adder
• Cascade four full adder
• Classical method 9 variable input needs 29 512
  line of truth table
• Cascading method can be expanded to greater
  number. Example 16-bit parallel adder

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Combinational Circuit Arithmetic Circuit

• Usage Poling system (for 6 person)
• Use full adder and parallel adder 4-bit (binary)
• Each full adder can add 3 polls

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Combinational Gates Arithmetic Circuit

• Adder-Subtractor
• Use twos complement
• X-YX(-Y)
• Twos complement for Y invert each Y bit and
  add 1

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Combinational Gates Arithmetic Circuit

• BCD Adder
• Classical method needs 29 lines in TT
• As a replacement, we use binary adder with a
  little alteration

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Combinational Gates Arithmetic Circuit

• BCD Adder
• Strategy
• Use 4-bit parallel adder to ad 2 BCD code
• If answer lt10, therefore it is correct (just
  leave it)
• If answer 10, therefore some calibration is
  needed to get to correct C, S8, S4, S2 and S1.
  Repeat this strategy for other 4-bit parallel
  adder

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Combinational Gates Arithmetic Circuit

• When answer lt10, therefore total BCD total
  Binary, no calibration is needed
• When answer 10, therefore
• Calibration
• Total BCD Total Binary requirement for
  calibration
• CKZ8.Z4 Z8.Z2

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Combinational Gates Arithmetic Circuit

• Comparator
• Magnitude comparator compare two value A and B
  to ensure if AgtB, AB or AltB
• Classical method need 22n line in TT
• Explore dissimilarity
• How we compare two 4-bit value A(a3 a2 a1 a0) and
  B(b3 b2 b1 b0)
• If (a3gtb3) therefore AgtB
• If (a3ltb3) therefore AltB
• If (a3b3) therefore AB and so on..

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Combinational Gates Arithmetic Circuit
A3B3

• A3

x3
A3 B3
B3
A3B3 x3A2B2 x3x2A1B1 x3x2x1A0B0
A2
x2
B2
(AltB)
A1
x1
A3B3 x3A2B2 x3x2A1B1 x3x2x1A0B0
B1
A0
x0
(AgtB)
B0
(AB)
x3x2x1x0
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Combinational Circuit - Arithmetic Circuit

• Comparator

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Combinational Circuit MSI Circuit

• There are four useful MSI circuit
• Decoder
• Demultiplexer
• Encoder
• Multiplexer
• Block Diagram

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Combinational Circuit MSI Circuit

• DECODER
• Codes used for representing entity, e.g. your
  name is a code which represent yourself (entity)
• This code can be identified (or decoded) using a
  decoder Provide code, identify entity
• Change binary information from n input line
  (maximum value for) 2n output line
• Is known as line decoder n to m, or nm or nxm
  decoder (mlt2n)
• Might be used to generate 2n (or less) minterm
  for n input variable

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Combinational Circuit MSI Circuit

• DECODER
• Example if code 00, 0, 10, 11is used to identify
  four bulbs, therefore we need 2-bit decoder
• This is 2x4 decoder which select output line
  based on the given 2 bit.
• Truth table

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Combinational Circuit MSI Circuit

• DECODER
• From the truth table, decoder circuit 2x4 is
• Notes each output in 2 variable minterm
  expression (XY, XY, XY, XY)

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Combinational Circuit MSI Circuit

• DECODER
• Design of 3x8 decoder
• Usage? Conversion from binary to octal

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Combinational Circuit MSI Circuit

• DECODER
• In general for n-bit code, decoder suppose to
  select up to 2n line

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Combinational Circuit MSI Circuit

• DECODER Function execution
• Boolean function in SOM for can be executed with
  decoder (to generate minterm) and OR gate (used
  for forming sum)
• Any combinational circuit with n input and m
  output can be done with n2n decoder and with m
  OR gate
• Good for circuit with a lot of output, and each
  function is express with several minterm

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Combinational Circuit MSI Circuit

• DECODER Function execution
• Example Full Adder

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Combinational Circuit MSI Circuit

• DECODER with Enable
• Most decoder has an enable signal, therefore it
  only active when enable, E1
• Truth table

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Combinational Circuit MSI Circuit

• DECODER with Enable
• In MSI, enable signal for decoder is zero enable,
  E, therefore this device only active when
  enable E0

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Combinational Circuit MSI Circuit

• LARGE DECODER
• Large decoder can be built using small size
  decoder
• E.g. 38 decoder can be built using 24 (with 1
  enable) as the following

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Combinational Circuit MSI Circuit

• LARGE DECODER
• E.g. 416 decoder can be built using two 38
  decoder (with 1 enable) as the following.
• How can you build 416 decoder by using 24
  decoder with enable?

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Combinational Circuit MSI Circuit

• ENCODER
• Encoder is the inversion of decoder.
• Several sets of input line, select one, it
  produce similar code for selected line
• Consist of 2n (or less) input line and n output
  line
• Created from OR gate
• Example

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Combinational Circuit MSI Circuit

• Truth table