6.8 Di.g.t!..,ttl. Electron.

i,cs

6-8 BGHB tie s©w@ffi s@grmeeRE& st!iae!`f*:®di©£d .

EI
Figure 6.9 showsthe BCD to sev.en f
segment decoder. BCD to seven segme,nt.
decoder \driver ICs are used to convert
i.tthe BCD signal into fo`rm. suitable, -for
driving these displays. In this sections,
we ale. going. to study LED.. and LCD
d.ecdders/drivers for seven `segment
displays. Let us tabulate the segm{3nt5,
activated during. e.ach digit display. .Fig.
6.8 biiows the 7 segment display. fr.§€j..6.8 Seven se.ginerlt disp!a`}f

The binary digit 1 is activat.e i`.he I,E.D for r,orresponding digit

common Oath.o.de seven segmeii.t clispl€iy ar,td thc bii}ary digit 0 is activ€ite. the`
LED for corresponding digi.t in the common &nod.e £.even se.gment d..i,splay.
iJ=

The following d.esig.n of BCD lo set/en segment displa.y c}.e{}t`jdei. is

desiiJgned for common cathode.. segmg.nt display.
1
~1

. .` Thbi® S.5 Truth table t.or BOD to se\Jen segment ciec;ode`r

.,,,-,.,,

01`j

1 011

t,
0.

1
I
 Decoder, Encoder and Code Corrverters 6.9

K-Map Sin.plificatiom

Expression for a Expression for b

CD oo I

1+
01

3,1-2+111
11 110 00 01
3fiJ 11
2
10

00-0111,10
_1`10 _1J
5T1-i 7Tll
.`

4 61!I 5 7ili 6
'4!1 :

1fx- 1:xJ `Lx+ 13 14

tx ix!
X .
X

rll `ix `i[x„9 1 8rllj 9-- `tx, 1P_

|JL - i.
1 xl\
I

a = A + C + BD + B'D' b = 8' + C'D' + CD \

Expression for a Expression for d

CD oo o| 11 10 CDoo, 01 !|1 I iu I
'800011110
0,1 :TiTTLili 2 0_1J 1 3il_1 I:f=
00

4rl 5T 7_ 6- 4L__ 5Tll 7 61111

11~- 11 011110

•1*.Lx-
„ix! 14__xJ 12fx EL_X
_xi15 txJ X
811 9LIL 8+111 1[x_ 'pEXT,,
--
10 X 9 1

_xJ11
I,

c -8 + C' + D d = B'D' + CD' + BC'D + B'C + A

Expression for e
Expression for f
CD oo o| 11 10
>CDoo] o| 11 !10 18-00011110
01!_J 1I 3 2flll 1 3 2 \
00

4 5 7 6!1i
FT`i ii`, 7 6,1,
0111,10

!+
1213 15 `lxi `[x] 4i t5- 1+x`
X y\ X X
_J X
1
givll
-__ _ __ 119
1lrxJ qllJ 1- 9
_1_i___

10_xJ
X X-
1111111111111111111_

1!

e -B,D, + CD, f = C'D' + BC' + A + BD'

6.J{3 Digital Electronic`s

Expression for g
C Doo 01 .11 10.
100011'110
0. 1 3L1 2[1]

7 6 11!

iri=i.'I `
f[x= fry t5lL-
X
_X, Tx'i
'[,(, -31:x-i
!91--
.
L|'1-
\
g = A + BC' + B'C + CD'
\
A,

AB CD

I
111111111111,1111111-111111

''--

c,D,
- I -- --L.

_->, I

-_}

\ a'
\
-
I_-
BC'

BD'

Fig. 6.9 Bcr] to seven segme nt decoder

 6.16 Digital Electronics

Solution:
We can implement BCD to 7 se,gment decoder for common anode as
follows.
Truth table for BCD.to seven s®grmeltt decoder

Digit \ A 8 C D a b C d e f 8

rlLJ(IIiiI-.E1E') `0 0 0 0 1
0 0 1 1I0 0 1 0 1 •0 010I010101 010 10 0 0 0 0 01I0 0 0 I0 0 0 0 010 10 I0 0101'i10I01 01 I0 010 1 0 0 10

6]13 code c®nverteF

Code converter is a combinational logic circuit to convert one form of
code to another form of.code. Some of these codes are binary coded decimal,
Excess code, Gray code and so on. Many i.imes it is required to convert
to another.
.13®1 Binary to BCD Convertei.
A code converter combinationa] a,ircuit i s designed to convert bin.ary to
BCD code. Fig 6.15 shows the ligic diagram of Binary to BCD code
converter.
The input code of code converter is binai.y.The output code of code
converter is BCD code.
 Decoder, Encoder and Code Corrverters 6.17

Fig Ex. 6.4

TFuth Table
Binary code BCD Converter
D CBA 84 83 82 a, Bo

0 000 0 0 0 0 0 I
I1

0 0 0 1 0 0 0 0

0 0 1 0 0 0 0 1 0

0 oil 1 0 0 0 1 1.

0 1 0 0 0 0 1 0 0

0 1 0 1 0 0 1 0 1

•0 0
0 1 1 0 1. 1
\0.
0 i 1 •1
0 0 1 1 1,

1 0 0 0 0 1 0 0 0

1 0 0 1 0 1 0 0 1

1 •0 1 u 1 0 0 0 0
1 01 1]100 1 0 0 0 1

1 1 0 0 1 0

1 1 0 1 1 0. 0 1 1

0 0
1

I
1 1

1]1-,---
0
1-
1 0
0
I

I 0 1

C9
6.]8 Digital Electronif s

K-Map Simplification

Expression for Bo
ExpF`Sssion for a,
BA oo 01 11 10

0. 1rl- Lil 2 0- f:1_ 211

00011110 @')

4 5!1 7-=i! 6
tt`9 o1
4~ I_= 5i '}`Str
I.

il
6
I

1.I.

1_ _J
12 `lpl '§1i 14 12 13 15 14

1-1 =lj
8 91,_ 10 8 9 1 10

_1J1

\ Bo-A 8, = DCB' + D'B

Expression for 82 Expression for 83

8 Aoo 01 11 10 `L7n oo 01 11 10

0 1 3 2.
0 1 3 2
0001111C'
00011110

4 11 5i- 7I 6I 4 5 6

12 13 `51 `41J 12 "-8r,:-I1:.-a_-13 15 14

8 9 1 10

L1:;i` 10,

82 = D ` C+ CB 83 -DC , 8 '

Expression for. 84
BA
C00011110
0

4
oo

5
-1
o|

- 7
.i|

B6
10

12 -1-
13 15

8
11
9 ``11
I, =j 10JJLJ

84 = DC + DB
 Decoder, Encoder and code converters 6.19

`.Logic Diagram

Binary code

D C a A.

Fig 6£15 Logic c!iagram of Binary to BOD code converter

C3)
 Electron.ics

.2 BCD to Excess -3 Code Converte'r

A code converter combinational circuit is designed to `C6nvert 'BCD
code to Excess - 3 code. The input code of code col-iverter is B,CD code.The
output code of code converter is Excess-3 code. Fig 6.16 shows the logic
diagram ofBCp to excess-3 code converter `
Truth Table

BCD Code E,xcess-3 Code

Decimal 83 82 a, Bo E3 E2 E, F`o

0, 0 0 0 0 0 0 1 1

1\ 0 0 0 1 0 i 0 0

2` 0 0 1 0 0 i 0 1

3, 0 0 1 I 0 1 1 0
'1
4 0 1 0 0 0 1 1

5 0 1 0 1 1 0 0 0

6 0 1 1 0 1 0 0 1

7 0 1 1 1 1 0 1 0

8 1 0 .0 0 1 0 I 1

9 1 0 1 1 1 0 0
10

The unused states are 1010,loll,1 I 00,1101,1110 and 1111. .So place
X (Don't Care C.ondition) for the corresponcli.iig . t>!!s.

K-Map Simplification
Expression for E3 E,xpression for E2
B,Bo oo 01 11 .1° B'Booo i ol 111 1o I
8200011110
0' \ 11 3 2
12000
lilt_ 3 2JJ®
11

4 5 rl_ 7 6_11 4,rll 7 6

`rx
I_1_+_
1:x]
0''1110

H
er ___ _1?x!`+J
13 15 14

tx_ X
9rl-
X X
`grxl
X

811_ 9 `1 `Lx'J`
- 1X a
x`l
11,ll,I,,,ll,,,I,,ii I
'E2 = 8,.a, ' Bo ' + P2 ' Bo+82 ' 8]
E3 = 83 + 82(Bo + 8,)
•=828, ' Bo ' +82 ' (Bo+B,)
E3=83+82Bo+82B,
 Decoder, Encoder and Code Corrverters 6.21

Expression for E4 Exp.ression forEo a

BiBo oo 01 11 10

--
BiBo oo 01 11 10.
3=00011110
0 fll •1 3,rll 2 a2-00011110-
+i.___, 1 3 \

irl-_\,
4!1i 5 , . 4111 5 6`i\__I,

ill
13 14 12 13 15 14__

X X XI X X
ix; ix! `10Li_ IX`I
8L1,I 9 81i_J 9 1 1X 1lx_
lxJ
Et = 8] ' Bo ' + B]Bo = Bp Bo Eo - Bo ,

Logic Diagram

83 82

-
81 8o

Eo

-11. '\E1

t
+

' \ 2,.
I

E3

Fig 6.16 Logic diagram cjf BCD tct Excess-3 code converter

`C5) \

-tlu-j|--ramp->+.t-Ld.---\
 \
6.22 Digital Electronics

xcess-3 code to BdD Code comveE.tel'

code converter combinatiorial cii.cuit is desig-ned to convert Excess -
to BCD code. The input code of code converter is Excess -3.The
output code of code converter is BCD code. F`ig 6.17 shows the logic
diagram of excess -3 code to BCD code converter.
Truth Table

Excess-3 B£ES Code-\

E3 E2 E, Eo 83 B2 81 Bo

0 0 1 1 0 0 0 0

0 1 0 0 0 0 0 1

0 1 0 1 0 0 1 0

0 1 1 0 0 .0 1 i

1 1 I o. 1 0 0,
\01
0, 0 0 0 1 0 1

\1
0 0 1 0 1 1 0

1, 0 1 0 0 1 1 1

1 0 1 1 I 0 0 0

1 1 0 0 1 0 0 1

The unused states are 0000, 0001, 0010,1101,1110 and 1111. So place
X (Don't Care Condition) for the corresponding above cells.
K-Map Simplification

Expression for Bo E%pression for 84

EiEo oo 01 11 10.

-xl,
EtEo oo 01 11 10
:3E2-00011110-
1 X 2rx-1 3E}oOoO+x 1rl!Xl 2rxl

4 11I 5 61•11 / 6 !1i

ill
_i 5_ _

re\1! T3______ 14 12 1!xl 15 `!xl

X X Ix+ 1.1! X
+
i _ '| 1 J
8._1J` 9 1 8 911J 1X
X 10
11_
Bo - Eo , 8, = E, ' Eo + E,Eo ' = E,® Eo
 Decoder, Eneoder and Code Corrverters. 6.23
\

Expression for 82 Expression for 83 \

EtFooo 01 i 11 10 E,Eo oo 01 11 10
---:-J3
?|x_ 1_xJ
9E=00011110 3,00011110
2 X 0 X 2 X
FT
4 1 5 6 4 5 7 6

rl-`!
`qlx,liTxl 'fl=
iF___. 13 X
x-- :x= ELxl_J
LilI 1 .X `',1J 8 9
'11|J
10

;ri-I
82 = E2.' Ei ' + E2EiEo + E3E,Eo ' 83 = E3E2 + E3E,Eo

ELogic Diagram

E3 E2 Ei i:o

\Bo
--

I.81
I

82

'!II_,

~ -i--- I +

L 83

I II

Fig 6.17 Logir, dia€j-ra.r., ot' Excess-3 to BCD code convertei

`CP
6.24 Electronics

Binary code to gray code co.mver6er

A code converter combinational circuit is designed to convert binary to
Gray code. Fig 6.18 shows the logic diagi`am ot. Binary to gray code
converter. '
The input code of code converter is binary.
The output code of code ,converter is Gi.ay code.
Truth Table .
Binary code Gray code
D
__0
C 8
_0
A G-J .G2
G, Go

0 0 0 0 0 0
0 0 0 1 0 0 0 1

0 0 1 0 0 0 ] 1

0 0 1 1 0 0 1 0
0 1 0 0 0 1 1 0
~1

0 1 0 1 0 1^ 1^

0 1 1 0 0 1 0 1

0 1 1 1 0 1 0 0
'1 0 0 0 1 1 0 0
0 0 1 1 i 0 1
\1
1 0 1 0 1 1 1 1
`1`
0 1 1 1 1 I 0
1 1 0 0 1 0 1 0
•1
I 0 1 1 0 1 1

1 1 1 0 1 icf 0 1
'J,0 0
1 1 1 1
11

K-Map Simplification
Expression for.Go Expression for G4
BA oo o| 11 10 *8'\ oo -1 01 , 11 10
C00011110
0 'rll 3 2'T1`l
C00011110
0 311_ 2_1J

4 6!1i 4 r'1 5il 7 6

11!
_i_2 _
`il! 15 14,1 i 13_1J 15 14

8, 9'|1J 11 `O'JJ
!`11-
9 ``r trll
iF
'1

G\o=8'A+BA'=8®A t-i ` = cB ' + a, ' 8 = c ®8

 \

Decoder, Encoder and Code Converters 6.25

Expression for G2 Expression for G3

BA oo 01 11 10 BA oo 01 11 10

6_ 2
00011110
1
13--- 00011110
0 1 3 2

4 r:i 5- 7- --~,6I_1r\ 4 5 7 6

1_ - 1
-- ,-,~_J
|r5__ 1514i
1

12rl- lie__-,- 15---1 14_11

-
12

8f a_-1 L=1 I
:.11_ 9 1-
- -- :,) - -- _1J
11

1
101

G2 = D ' C + DC ' = COD

We get the simplif'ied boolean expression for the code convertor of
Binary to Gray code. `

Go = B'A + BA' = 8 ® A

G{ =Lij +C'B=C®B

G2 = D'C + DC' = C®D

G3-D
By using the €`.bove expression we can construct the binary to gray code
convertor as follows.
Eiogic Diagram
DC

F§g 6.18 Logic diag!am of Binary to gray code convertel-

.f:`
____=±==±SEfi-JE±±===c=+==__:-±---F±_:_------

E=
a

»,

6.26 Digital Electronics

G-ray code to Binary coda, comveRTtreF

A code converter combinatjonal circuit is `iesigned to convert gray code
to binary code. The input code of code converter js BGray. The output code
of code 8onverter is binary code. Fig 6.19 shows ,tl'i.e logic diagram of gray to
binary code converter.
\
Truth Table

. Gray code Binary code

tiBo
G3 G2 G, Go 83, 8?, 8,

0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 1 0 0 1 0

0 0 1 0 0 0 1 1

0 1 1 0 0 1 0 0

0 I 1 1 0 1 0 1

'0 1 0 1 0 1 1 , 0

\o 1 0 0 0 I 1 1

\I
1 0 0 1 0 0 0

1 1 0 i 1 0 0 1
I1

1 1 1 1 0 1 0

1 I 1 0 1 0 1 1

1 0 1 0 1 I 0 0

1 0 1 1 1 1 0 1

1 0 0 I 1 1 1 0

1 0 0 0 1I 1]iI---, 1 1
 1

-+I

Decoder, Encod.er and Code corrverters 6.27

'
K-Map Simplification

Expression for 8o Expression for 84

G,Gooo 01 11 10 G,Gooo . ol 11 10
'900011110
0 `clJ 3 2[1] '300011110
0 , 1 3r- 2-i
11_ _1J,
4cJ 5 7rl`'\J 6 4.rl- 5-11 6

1_ _J
12 `rlr` 15 1?~11 12 .
1rl`-1_
83 9
|J 1[)
|.J
8[1ItlJ, E3
1 , 10'

illI

Bo = (G3'G2+ G3G2'`) G] C.o` + fG33::G2` + G3 G2) Gi' Go +

(G3' G2.+ G3 G2') Gi Go + (G3' .G2` + G3 G2) Gi Go')

J,

= (G3 ® G2) G] ' Go`' +(G3 0 G2) G] ' Go +

(G3 © G2) G] Go + (G3 0 G2) Gi Go'

= (G3 ® G2) (G] ` Go.. + G]Go) +.G3 0 G2 ) ( G, ' Go. + G} Go)

= (G3®G2)(Gi oGo)+(G3 0G2)(G,®Go) .

= (G3®G2)(Gi®Go)`+(G3®G2)' (Gi®Go) `

= (G3 ® G2) ® (Gt ® Go)

Bi = (G3.. G2' + G3G2)Gi + {.G., G2 + G3 G2') Gi '

= (G3 0 G2) Gi + (G3 ® G-2) Gi `

•= (G3 © G2)' Gi + {G3 © G.1) Gi `

-G3 ® G2 ® a,

C9
\'?`.

6.28 Digital Electronics

Expression for 82 EL}.€EL'il!*e§Sion for 83

G,Gooo
'300011110
0 1
ol

3I
11
-2i
10

4r- 6-- 7r-- 6T

'11_ -- - - -r..i J
1 1

12 13 15 14

8rl- 9-1-FTr toll .`-.....I,.

\ 1_ -r,, - , OI-- 11-,-_J W

82 = G3'G2 + G3G2' 83 - G3

-G3© G2

Logic D`iagrarm

G3 G2 Gi G;
i

I-i-_ ==::===.:;)L=\
i+'I

!ELi

i ji=
`+I+`.-..--.`. -`\
-~`\

.-=i;i-~.-~,,/I--,.-.--------.--------82

-.---1-.-~-.*-~`

Fig 6.nl9 Logic diagram of Gra`,/ J:;,`}de to Binary coc!et

converter

` t` A ir ` \IHqE[dHit[H