Combinational Circuit – Arithmetic Circuit

1MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR

Combinational Circuit – Arithmetic Circuit

• Parallel AdderExample: 4-bit adder

MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR

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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 two’s complement

X-Y=X+(-Y)– Two’s complement for Y = invert each Y bit and add 1


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

alteration


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BCD Adder• Strategy

– Use 4-bit parallel adder to ad 2 BCD code– If answer <10, 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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• When answer <10, therefore total BCD = total Binary, no calibration is needed

• When answer ≥10, therefore CalibrationTotal BCD = Total Binary + requirement for calibrationC=K+Z8.Z4 +Z8.Z2


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• Comparator– Magnitude comparator: compare two value A

and B to ensure if A>B, A=B or A<B– 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 (a3>b3) therefore A>B– If (a3<b3) therefore A<B– If (a3=b3) therefore A=B and so on..


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A3

A2

A1

A0

B2

B1

B0

B3

x3

x2

x1

x0

A3 B3’

A3’B3

(A<B)

(A>B)

(A=B)

A3’B3 + x3A2’B2 + x3x2A1’B1 + x3x2x1A0’B0

A3B3’ + x3A2B2’ + x3x2A1B1’ + x3x2x1A0B0’

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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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 n:m or nxm decoder

(m<=2n)• Might be used to generate 2n (or less) minterm for n input

variable


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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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DECODER• From the truth table,

decoder circuit 2x4 is• Notes: each output in 2

variable minterm expression (X’Y’, X’Y, XY’, XY)


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DECODER• Design of 3x8 decoder

• Usage? Conversion from binary to octal


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DECODER• In general: for n-bit code, decoder suppose to

select up to 2n line


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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 n:2n 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 CircuitDECODER – Function execution• Example: Full Adder


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Combinational Circuit – MSI CircuitDECODER with Enable• Most decoder has an enable signal, therefore it

only active when enable, E=1• Truth table


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Combinational Circuit – MSI CircuitDECODER with Enable• In MSI, enable signal for decoder is zero enable,

E’, therefore this device only active when enable E’=0


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Combinational Circuit – MSI CircuitLARGE DECODER• Large decoder can be

built using small size decoder

• E.g. 3:8 decoder can be built using 2:4 (with 1 enable) as the following


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Combinational Circuit – MSI CircuitLARGE DECODER• E.g. 4:16 decoder can

be built using two 3:8 decoder (with 1 enable) as the following.

• How can you build 4:16 decoder by using 2:4 decoder with enable?


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Combinational Circuit – MSI CircuitENCODER• 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 CircuitTruth table

Combinational Circuit – Arithmetic Circuit

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