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Design and simula ion o e icien combina ional ci cui s based on a new XOR s uc u e
in QCA echnology
© 2021 he Au ho s
Published e sion
Sa aiezadeh, Beh ouz; Mahdipou , Eb ahim; Haghpa as , Majid; Sayedsalehi,
Sami a; Hosseinzadeh, Mehdi
Sa aiezadeh, B., Mahdipou , E., Haghpa as , M., Sayedsalehi, S., & Hosseinzadeh, M. (2021).
Design and simula ion o e icien combina ional ci cui s based on a new XOR s uc u e in QCA
echnology. Op ical and Quan um Elec onics, 53(12), A icle 684.
h ps://doi.o g/10.1007/s11082-021-03294-z
2021
Vol.:(0123456789)
Op ical and Quan um Elec onics (2021) 53:684
h ps://doi.o g/10.1007/s11082-021-03294-z
1 3
Design andsimula ion o e icien combina ional ci cui s
based onanew XOR s uc u e inQCA echnology
Beh ouzSa aiezadeh1· Eb ahimMahdipou 1· MajidHaghpa as 2 ·
Sami aSayedsalehi3· MehdiHosseinzadeh4,5
Recei ed: 27 May 2021 / Accep ed: 10 Oc obe 2021
© The Au ho (s) 2021
Abs ac
Quan um-do cellula au oma a (QCA), due o i s unique cha ac e is ics like low powe
consump ion, nanoscale design, and high compu ing speed is conside ed as an eme ging
echnology, and i can be used as an al e na i e o CMOS echnology in ci cui design
o quan um compu e s in he nea u u e. XOR ga e has many applica ions in he design
o digi al ci cui s in QCA. In his pape , an e icien no el s uc u e o XOR ga e is p o-
posed in QCA. Also, a no el 1-bi compa a o ci cui , 1-bi ull adde , bina y o g ay and
g ay o bina y con e o code based on he p oposed XOR is designed and simula ed using
QCADesigne 2.0.3. The simula ion esul s demons a ed ha he p oposed s uc u es p o-
ide imp o emen s compa ed o p e ious wo ks in e ms o QCA cells coun , a ea, and
ci cui cos .
Keywo ds Quan um-do cellula au oma a· XOR ga e· Compa a o · Full adde ·
Con e e
1 In oduc ion
Powe consump ion and ci cui size educ ion a e he majo p oblems in digi al elec onics.
CMOS echnology ha is used o design hese ci cui s nowadays has p oblems such as high-
powe consump ion, leakage cu en and sho -channel e ec s (Len e  al. 1993). Landaue
(1961) s a ed ha o any bi o in o ma ion loss, he e is a KTln2 Joules o ene gy dissipa ion
* Majid Haghpa as
[email p o ec ed]
1 Depa men o Compu e Enginee ing, Science andResea ch B anch, Islamic Azad Uni e si y,
Teh an, I an
2 Facul y o In o ma ion Technology, Uni e si y o Jy äskylä, P.O.Box35,
FI-40014Uni e si yo Jy äskylä,Jy äskylä, Finland
3 Depa men o Compu e Enginee ing, Sou h Teh an B anch, Islamic Azad Uni e si y, Teh an,
I an
4 Men al Heal h Resea ch Cen e , Psychosocial Heal h Resea ch Ins i u e, I an Uni e si y o Medical
Sciences, Teh an, I an
5 Compu e Science, Uni e si y o Human De elopmen , Sulaymaniyah, I aq
B.Sa aiezadeh e al.
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684 Page 2 o 16
and his in o ma ion canno be e ie ed in any way. This made esea che s hink abou an
al e na i e o CMOS. This new echnology should ha e cha ac e is ics such as smalle size,
highe speed, and lowe powe consump ion han CMOS echnology wi h same unc ionali y.
In 1944, Quan um-do cellula au oma a (QCA) wi h same unc ionali ies o e ed by Tougaw
and Len (1994). QCA Cell is he main and undamen al uni o QCA echnology. Each QCA
cell includes ou quan um do s and wo ee elec ons (Zhang e al. 2004). Logical ze o and
one s a es in his echnology is de e mined by he loca ion o elec ons in he cells.
The mos pe manen s a e o a QCA cell is when wo elec ons a e diagonal in cell. XOR
ga e is used as based ga e in logic and combina ional ci cui s design, like mul iplexe (Sen and
Du a 2014; Rashidi e al. 2016), Con e e s (Beigh and Mus a a 2014), Full Adde (Ahmad
e al. 2014; Shams and Bayoumi 2000; Hänninen and Takala 2010; Kianpou e al. 2014), as
well as Compa a o in QCA (Failed 2020a; Shi i e al. 2019). The e o e, he design o QCA-
based XOR s uc u e has been conside ed by esea che s in ecen yea s. The co e idea o his
s udy, is he o e ing o new QCA-based h ee-inpu XOR and wo-inpu XNOR s uc u es. To
show ha ou p oposed XOR s uc u e is be e han p e ious s uc u es, we use his s uc u e
o design a Full Adde , 4-bi bina y o g ay (B2G) code con e e , 4-bi G ay o Bina y (G2B)
code con e e , and single compa a o ci cui , and compa e he esul s wi h p e ious wo k.
The p oposed designs a e simula ed by QCADesigne and compa ed o he p e ious wo ks.
The majo con ibu ions o ou wo k can be summa ized as ollows:
• An e icien h ee-inpu s XOR ga e is p oposed.
• A no el Full Adde based on he p oposed XOR is sugges ed and designed.
• A no el single bi Compa a o based on he p oposed XOR is sugges ed and designed.
• A no el B2G code con e e based on he p oposed XOR is sugges ed and designed.
• A no el G2B code con e e based on he p oposed XOR is sugges ed and designed.
• Simula ion o he p oposed s uc u es by QCADesigne 2.0.3 (Walus e al. 2004) is done.
• The p oposed ci cui s imp o ed in numbe o cells, occupied a ea and la ency compa ed o
p e ious wo ks.
• Ou 1-bi simple p oposed s uc u es ha e no c osso e .
• Ou 1-bi scalable p oposed s uc u ed ha e c osso e .
• The o al ene gy dissipa ion o p oposed designs o 1-bi compa a o is calcula e by
QCADesigne -E (h ps:// gi hub. com/ FSillT/ QCADe signe -E).
The s uc u e o his pape is o ganized as ollows: In Sec .2, he p e ious wo ks a e dis-
cussed. Sec ion3 o e s he new s uc u es o XOR and XNOR ga es, as well as One-bi Com-
pa a o ci cui , Full Adde , 4-bi B2G con e e , and 4-bi G2B con e e based on hem. In
Sec .4, he simula ion esul s will be depic ed. In Sec .5, he p oposed ci cui s will be com-
pa ed wi h p e ious wo k. Finally, he Conclusions and u u e wo ks a e p o ided in Sec .6.
2 P e ious wo ks
In his sec ion, a numbe o s udies conduc ed in ecen yea s a e e iewed. Ak e e al.
(2015) o e ed wo compa a o ci cui s using hei p oposed TR and QCA-based Feynman
ga es. The designed ci cui s using TR ga e has 134 cells, 0.25 µm2 a ea, and 0.5 Clock
Cycle la ency; and he design using Feynman includes 87 cells, 0.11 µm2 a ea, and 0.5
clock cycle la ency. Shi i e al. (2019), p oposed and simula ed a 1-bi compa a o using
Majo i y, XNOR, and NOT ga es in QCA echnology. Thei p oposed design has 38 cells,
Design andsimula ion o e icien combina ional ci cui s…
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Page 3 o 16 684
0.03 µm2 o a ea, as well as 0.5 cock cycle la ency. Ahmed e al. (2020a), in oduced wo
QCA-based 1-bi compa a o ci cui s. The i s design has 55 cells and 0.0669 µm2 o a ea,
and he second one has 42 cells and 0.0407 µm2 o a ea. Majeed e al. (2020b), o e ed new
QCA-based XOR and XNOR ga es wi h ewe cells and smalle a eas compa ed o he
exis ing designed ga es. Also, hey designed h ee one-bi compa a o ci cui s wi h p o-
posed s uc u es. The designed compa a o s ha e 40, 35, and 33 cells, and he occupied
a ea a e 0.05, 0.04, and 0.04, espec i ely. The la ency o he p oposed designs was 0.75
clock cycle and he ci cui s we e I e e sible. Sa e e al. (2020c), p oposed QCA-based
one-bi compa a o using 3 Majo i y ga es and a NOT ga e. The p oposed ci cui includes
30 cells, and he occupied a ea is 0.05 µm2 and he la ency is one clock cycle. This ci cui
was op imal in e ms o cell coun s, bu i was no sui able in e ms o a ea compa ed o
p e ious wo ks. Balali e al. (2017), designed a Full Adde using 3-inpu s XOR. The p o-
posed XOR consis ed o 14 cells, wi h an a ea o 0.01 µm2 and a la ency o 0.5 clock cycle.
Roshany e al. ( 2019), p oposed a 3-inpu s XOR, and hen by exploi ing i , hey designed
and simula ed a QCA-based mul i-laye Full Adde . Majeed a el. (2020a), p oposed a Full
Adde using a no el XOR ga e. The simula ion esul s shown ha he p oposed design was
be e han p e ious wo ks. Babaie e al. (2018) p oposed a QCA Full Adde . The p oposed
ci cui had only 26 cells and he ou pu s needed wo clock zones o gene a e. Zhang e al.
(2017), p oposed a new- i e majo i y o cons uc Full Adde s. The p oposed Full Adde
had 35 cells and occupied a ea 0.0288, and also 1 clock cycle delay. Islam e al. (2018),
p oposed a new QCA ci cui o con e 4-bi bina y o 4-bi B2G and 4-bi G2B code using
wo inpu XOR ga e. The p oposed QCA B2G and G2B ci cui s has 37 and 47 cells, and
0.04 and 0.05 he occupied a ea, espec i ely. Ka kaj e al. (2016), p oposed a new XOR
ga e and also non- e e sible 4-bi B2G and G2B con e e based i in QCA echnology.
Shu e al. (2020), p oposed a new 4-bi B2G con e e by employing he p oposed no el
XOR s uc u e as a basic building block in i s ci cui . Ahmadpou e al. (2018), p oposed
a no el 1-bi Full Adde based on hei 3-inpu XOR s uc u e. This ci cui was simula ed
by only 20 cells and equi ed h ee clock zones. Nu iddin e al. (2019), p oposed new XOR
s uc u es and designed based on hei simple and scalable Full Adde s. The scalable o m
had 49 cells and ou clock phases. Also, simple o m had 35 cells and wo clock phases.
Sha ma e  al. (2020), p oposed 1-bi compa a o ci cui ha designed by only 26 cells.
Wang e al. (2020), p oposed a no el XOR/XNOR s uc u e o modula design o QCA
ci cui s. Then hey designed and simula ed 1-bi Full Adde and 1-bi Compa a o ci cui s
based on i . The design o 1-bi Full Adde used only 60 cells and had a delay o 0.75 clock
cycle. The design o 1-bi compa a o used 47 cells and had a delay o 0.75 clock cycle.
3 The p oposed s uc u es anddesigns
XOR and XNOR ga es ha e e y ex ensi e applica ions in design o combina ional and
sequen ial ci cui s o a i hme ic and logic uni s such as compa a o , ull adde , and B2G
con e e , G2B con e e , as well as Re e sible ga es like F edkin, To oli, Pe es, and
Feynman. Some o exis ing s uc u es ha e a la ge numbe o cells and a ea, and also
some ha e a long delay, which leads o an inc ease in he cos o he s uc u e and he
ci cui designed by hem. The e o e, design o such ga es in QCA has a signi ican and
c i ical impo ance. On he o he hand, wi h op imal design o XOR and XNOR ga es
in o de o use in combina ional ci cui s, we can ha e ci cui s wi h ewe cell coun s, as
well as smalle a ea and less delay. The unc ionali y accu acy o p oposed designs a e
B.Sa aiezadeh e al.
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684 Page 4 o 16
con i med using QCADesigne (Walus e al. 2004). In he ollowing subsec ions, new
QCA-based XOR s uc u e and also he Non- e e sible 1-bi Compa a o , Full Adde ,
B2G and G2B con e e s code a e p oposed.
3.1 No el XOR andXNOR S uc u es inQCA
A no el XOR s uc u e based on QCA echnology is designed and simula ed, as shown
in Fig.1. The inpu s a e A, B, and C, and Ou is used as he ou pu o he p oposed
s uc u e. The p oposed s uc u e can be used in design o logic and compu a ional ci -
cui s in QCA. This s uc u e has 10 cells, a ea o 0.01µm2, and 0.5 clock cycle delay.
I he alue o one o hese inpu s is se o −1, hen he p oposed s uc u e ope a es
as 2-inpu s QCA XOR. Also, i one o he inpu s is se o + 1, he p oposed s uc u e
will ac as 2-inpu s QCA XNOR. Fo ins ance, as illus a ed in Fig.2, by ixing one o
he inpu s, he s uc u e o his ga e becomes a 2-inpu s QCA XNOR ga e.
3.2 The p oposed 1‑bi compa a o
In digi al ci cui s, in addi ion o sub ac ion and addi ion ope a ions, some imes i is
necessa y o compa e inpu s. A 1-bi compa a o ci cui has wo inpu s namely A and
B, and h ee ou pu s namely G, E and L, which indica e ha he inpu A is la ge , equal
o smalle compa ed o inpu B, espec i ely. The G, E, and L ou pu s a e calcula ed
acco ding o ela ions in (1).
Fig. 1 The p oposed 3-inpu s
QCA XOR s uc u e
Fig. 2 The p oposed 2-inpu s
QCA XNOR ga e s uc u e

Design andsimula ion o e icien combina ional ci cui s…
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Page 5 o 16 684
In his pape , we p oposed 1-bi compa a o ci cui based on he logic diag am, as
shown in Fig.3.
The QCA s uc u es o p opose ci cui a e simula ed using QCADesigne 2.0.3 (Walus
e al. 2004) which is shown in Fig.4. The p oposed XNOR s uc u e, as well as Majo i y
ga e and NOT ga e is used in hem. Simple design#1 and design#2 o 1-bi compa a o
has only 25 cells and 0.02µm2 a ea, as shown in Fig.4a, b. The ou pu o hese designs
ob ains a e 0.75 clock cycle delay. These p oposed s uc u e ha e no c osso e . Howe e ,
hese designs o compa a o a e somewha di icul o ex end o an n-bi compa a o . The e-
o e, we also p opose a scalable o m o he compa a o . The scalable o m is composed o
35 cells wi h ou clocking phases. This s uc u e occupies an a ea o only 0.028 μm2, as
shown in Fig.4c.
3.3 The p oposed ull adde s
In his sec ion, new designs o ull adde in quan um-do cellula au oma a echnology is
p esen ed. The Full Adde ci cui is a basic uni in digi al a i hme ic and logic ci cui s. Full
Adde p oduces wo ou pu s (SUM, Cou ) by pe o ming addi ion ope a ion on h ee inpu s
(1)
⎧
⎪
⎨
⎪
⎩
L(A<B)∶AB,
E(A=B)∶A⊙B,
G(A>B)∶(A⊕B).
AB
Fig. 3 The logic diag am o he
p oposed s uc u e o a 1-bi
compa a o ci cui
Fig. 4 The p oposed 1-bi compa a o : a simple design#1 b simple design#2 c scalable design
B.Sa aiezadeh e al.
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684 Page 6 o 16
alues (A, B, Cin). We p opose wo QCA s uc u es o 1-bi Full Adde , as shown in Fig.5.
The s uc u e o he p oposed design has h ee inpu s (A, B, Cin) and wo ou pu s (SUM,
Cou ). These s uc u es a e simple and scalable designs. The p oposed XNOR s uc u e,
as well as Majo i y ga e and NOT ga e is used in hem. Simple design o 1-bi Full Adde
uses only 20 cells and 0.014 µm2 a ea. The ou pu o his design ob ains a e 0.75 clock
cycle delay. This p oposed s uc u e has no c osso e . Howe e , his Full Adde is some-
wha di icul o ex end o an n-bi adde . The e o e, we also p opose a scalable o m o he
ull adde o use as a ipple ca y adde (RCA). The scalable o m is composed o 29 cells
wi h 0.75 clocking phases. This s uc u e occupies an a ea o only 0.025 µm2, as shown in
Fig.5b.
RCA is an adde ci cui ha by se ially cascading 1-bi adde s is cons uc ed. A 2-bi
RCA calcula es he a i hme ic sum o wo 2-bi bina ies and he ci cui consis s o wo
1-bi ull adde ci cui s, as shown in Fig.6. The p oposed 1-bi ull adde s a e placed se i-
ally o success ully implemen he design o he QCA 2-bi RCA, as shown in Fig.6.
3.4 The p oposed 4‑bi B2G code con e e
Code con e e s a e ci cui s ha con e code in o ano he . In his sec ion, is p oposed
a no el QCA ci cui o con e he 4-bi B2G code. This con e sion me hod is use ul o
educe he apid swi ching ac i i y. The logical s uc u e o he p oposed 4-bi B2G code
con e e is depic ed in Fig.7. Inpu s a e desc ibed as A3, A2, A1 and A0 and he co -
esponding g ay ou pu s a e P3, P2, P1, and P0. The logical equa ion o 4-bi B2G code
con e e is
P3=A3,P2=A3
⊕
A2,P1=A2
⊕
A1and P0=A1
⊕
A0
.
The main componen o his con e e is XOR ga e. The p oposed XOR s uc u e is
used o simula ing B2G con e e . The QCA diag am o he p oposed 4-bi B2G code
con e e is depic ed in Fig.8. This s uc u e has 29 cells and 0.02 µm2 a ea. I needs wo
clock zones o gene a e he co ec ou pu s. Ou p oposed s uc u e has no c osso e .
3.5 The p oposed 4‑bi G2B con e e
In his sec ion, a no el design o 4-bi G2B code con e e based on he p oposed wo-
inpu XOR ga e in QCA is sugges ed. The logical s uc u e o con e ing 4-bi G2B code is
shown in Fig.9. Inpu s a e desc ibed as A3, A2, A1 and A0 and he co esponding bina y
ou pu s a e P3, P2, P1, and P0. The main componen o his con e e is XOR ga e. The
p oposed XOR s uc u e is used o simula ing G2B con e e . The QCA-based 4 bi G2B
Fig. 5 The p oposed Full Adde in QCA: a simple design b scalable design
Design andsimula ion o e icien combina ional ci cui s…
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Page 7 o 16 684
Fig. 6 The p oposed 2-bi RCA design in QCA
Fig. 7 The logical s uc u e o 4
bi B2G code con e e
Fig. 8 The p oposed s uc u e
B2G con e e in QCA
B.Sa aiezadeh e al.
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684 Page 8 o 16
con e e is shown in Fig.10. This s uc u e has 32 cells and 0.03 µm2 a ea. I needs wo
clock zones o gene a e he co ec ou pu s. Ou p oposed s uc u e has no c osso e .
4 The simula ion esul s o p oposed designs
In his sec ion, he simula ion esul s o p oposed XOR s uc u e, XNOR s uc u es, he
p oposed single bi Compa a o , Full Adde ci cui s, he p oposed 4 bi B2G and G2B code
con e e s based on QCA echnology a e shown. The simula ion esul o he p oposed
design o QCA XOR is shown Fig.11. In his igu e, A, B, and C a e inpu s and Ou is he
ou pu .
The simula ion esul o he p oposed design o QCA XNOR is shown Fig.12. In his
igu e, A and B a e inpu s and Ou is ou pu .
The simula ion esul o he p oposed design o single bi Compa a o is shown Fig.13.
In his igu e, A and B a e inpu s and L (A is less han B), G (A g ea e han B) and E (A
equal o B) a e ou pu s.
The simula ion esul o he p oposed design o Full Adde is shown Fig.14. In his ig-
u e, A, B and
Cin
a e inpu s and SUM and
Cou
a e ou pu s.
The simula ion esul o he p oposed design o 4 bi B2G code con e e is depic ed
Fig.15. I has ou inpu s which a e bina y digi s. The ci cui has also ou ou pu s which
a e he con e ed equi alen o he inpu ec o in o he g ay code.
Fig. 9 The logical diag am o 4
bi G2B code con e e
Fig. 10 The p oposed s uc u e G2B con e e in QCA
Design andsimula ion o e icien combina ional ci cui s…
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