Subtractor

PPTs on Subtractor

1. SYED HASAN SAEED
[email protected]
[email protected]
1
syed hasan saeed, Integral University,
Lucknow

2. BINARY SUBTRACTOR
RULESFORBINARYSUBTRACTION
0 -0 = 0
0 -1 = 1 with borrow 1
1 -0 =1
1 –1=0
NOTE:Inthesecondcase(0–1)itisnecessarytoborrowa1.
2
syed hasan saeed, Integral University,
Lucknow

3. TYPES OF BINARY SUBTRACTOR
•Half Subtractor
•Full Subtractor
Half Subtractor:
•It is a combinational circuit with two inputs and two outputs ( difference
and borrow)
•Two inputs are A (minuend), B (subtrahend) and two outputs are D
(difference) and B
o(borrow out).
•It is used to perform subtraction of two bits.
3
syed hasan saeed, Integral University,
Lucknow

4. BLOCK DIAGRAM:
LOGIC DIAGRAM:
HALF
SUBTRACTOR
D
B
o
A
B
D
B
o
A
B
4
syed hasan saeed, Integral University,
Lucknow

5. INPUTS OUTPUTS
Minuend(A)Subtrahend (B)Difference (D)Borrow (B
o)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0
TRUTH TABLE OF HALF -SUBTRACTOR
5
syed hasan saeed, Integral University,
Lucknow

6. INPUTS OUTPUTS
Minuend(A)Subtrahend (B)Difference (D)Borrow (B
o)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0
TRUTH TABLE OF HALF -SUBTRACTOR
K-Map for difference (D)
0 1
1 0
A
BBA BA
0 1
0
1
6
syed hasan saeed, Integral University,
Lucknow

7. INPUTS OUTPUTS
Minuend(A)Subtrahend (B)Difference (D)Borrow (B
o)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0
TRUTH TABLE OF HALF -SUBTRACTOR
K-Map for difference (D) K-Map for Borrow Output (B
o)
0 1
1 0
A
BBA BA
0 1
0
1
0 1
0 0
A
B
0
0
1
1BA
7
syed hasan saeed, Integral University,
Lucknow

8. From K-maps
syed hasan saeed, Integral University,
Lucknow
8BAB
BABAD


LOGIC DIAGRAM
A
B
D
B
o

9. DISADVANTAGE OF HALF SUBTRACTOR:
Halfsubtractorcanonlyperformthesubtractionoftwobinarybits.But
whileperformingthesubtraction,itdoesnottakeintoaccounttheborrowof
thelowersignificantstage.
HALFSUBTRACTOR USINGBASICGATES:
syedhasansaeed, Integral University,
Lucknow
9BA BA BABAD  BAB
O
 A B

10. FULL SUBTRACTOR:
•Full subtractor is a combinational circuit.
•It performs subtraction involving three bits (i) minuend bit (ii)
subtrahend bit (ii) borrow from the previous stage.
•It has three inputs (i) X (minuend) (ii) Y (subtrahend) (iii) Bin from
the previous stage.
•It has two outputs D (difference) and Borrow out Bout.
LOGIC SYMBOL:
syedhasansaeed, Integral University,
Lucknow
10
X
Y
Bin
D
Bout
FULL
SUBTRACTOR

11. TRUTH TABLE:
syed hasan saeed, Integral University,
Lucknow
11
INPUTS OUTPUTS
XYB
inDB
out
000 0 0
001 1 1
010 1 1
011 0 1
100 1 0
101 0 0
110 0 0
111 1 1
K-Map For Difference Output (D)
0 1 0 1
1 0 1 0
X
YB
in
00 01 11 10
0
1inininin
XYBBYXBYXBYXD 
K-Maps For Borrow Output (B
out)
0 1 1 1
0 0 1 0
X
YB
in
00 01 11 10
0
1 ininout
YBBXYXB 

12. syed hasan saeed, Integral University,
Lucknow
12inininin
XYBBYXBYXBYXD  in
inin
inin
BYXD
BYXBYXD
BYXYXBXYYXD



)()(
)()(
•Equationforaborrowoutputisresemblesthecarryoutputoffulladder
exceptthatoneoftheinputiscomplemented.
•EquationforDissameasthesumofoutputforafulladder.
•Itispossibletoconvertafulladderintoafullsubtractorby
complementingthatinputbeforetoitsappliedtotheinputofgateswhich
formtheborrowoutput.

13. RELIZATION OF FULL SUBTRACTOR:
syed hasan saeed, Integral University,
Lucknow
13
X YBin
D
Bout

14. THANK YOU
syed hasan saeed, Integral University,
Lucknow
14