design

1. Combinational Logic 1
DIGITAL LOGIC DESIGN
by
Dr. Fenghui Yao
Tennessee State University
Department of Computer Science
Nashville, TN

2. Combinational Logic 2
Remember
 Combinational
 The outputs depend only on the current input
values
 It uses only logic gates
 Sequential
 The outputs depend on the current and past input
values
 It uses logic gates and storage elements
Network
.
.
.
.
.
.
Inputs Outputs

3. Combinational Logic 3
Notes
 If there are n input variables, there are
2^n input combinations
 For each input combination, there is
one output value
 Truth tables are used to list all possible
combinations of inputs and
corresponding output values

4. Combinational Logic 4
Basic Combinational
Circuits
 Adders
 Multipliers
 Multiplexers
 Decoders
 Encoders
 Comparators
 Subtractors

5. Combinational Logic 5
Design
 Determine the inputs and outputs
 Assign a symbol for each
 Derive the truth table
 Get the simplified boolean expression
for each output
 Draw the network diagram

6. Combinational Logic 6
Example
 Conversion from BCD to excess-5

7. Combinational Logic 7
Example (Cont.)
CD
B
A
W 



8. Combinational Logic 8
Example (Cont.)
'
'
'
' BCD
C
B
D
B
A
X 




9. Combinational Logic 9
Example (Cont.)
diagram
network
the
Draw
Z
and
Find Y

10. Combinational Logic 10
Adders
 Essential part of every CPU
 Half adder (Ignore the carry-in bit)
 It performs the addition of two bits
 Full adder
 It performs the addition of three bits

11. Combinational Logic 11
Half-Adder
 You can use K-Map to simplify
 It is also obvious from the truth table

12. Combinational Logic 12
Full-Adder

13. Combinational Logic 13
Full-Adder
i
i
i
i
i
i
i
i
i
i
i
i
i
B
A
C
B
A
C
B
A
C
C
B
A
S






 '
'
1
HOW?????

14. Combinational Logic 14
4-bit Adder Implementation
From course book
0
0 
C

15. Combinational Logic 15
Question
 How can you get 32-bit implementation?

16. Combinational Logic 16
Binary Subtractor
 Remember
 You need to take 2’s complement to represent
negative numbers
 A-B
 Take 2’s complement of B and add it to A
 First take 1’s complement and add 1

17. Combinational Logic 17
4-Bit Adder and Subtractor
)
(
)
(
1
)
(
0
Overflow
V
Subtractor
M
Adder
M


From course book

18. Combinational Logic 18
Binary Multiplier
From course book

19. Combinational Logic 19
Comparators
 Compare two input words
 Returns 1 if
A=B, 0
otherwise

20. Combinational Logic 20
From course book

21. Combinational Logic 21
Decoder
 n by 2^n decoder
 Converts information from n input lines into 2^n
output lines
 2x4 Decoder
 3x8 Decoder

22. Combinational Logic 22
2x4 Decoder

23. Combinational Logic 23
Internal Structure of 2x4
Decoder

24. Combinational Logic 24
Another View

25. Combinational Logic 25
From
course
book

26. Combinational Logic 26
Example

27. Combinational Logic 27
4x16 Decoder
From course book

28. Combinational Logic 28
Full Adder with Decoder
i
i
i
i
i
i
i
i
i
i
i
i
i
B
A
C
B
A
C
B
A
C
C
B
A
S






 '
'
1

29. Combinational Logic 29
Multiplexers
 You can select information from one of
many input lines and assign it to one
output line
 You have input lines, control lines, and
one output line
 It is called MUX

30. Combinational Logic 30
2x1 Multiplexer

31. Combinational Logic 31
4x1 Multiplexer

32. Combinational Logic 32
Boolean Function
Implementation
How do you implement it with 8x1 MUX?

33. Combinational Logic 33
Example

34. Combinational Logic 34
Three-State Buffer

35. Combinational Logic 35
2x1 MUX with Three-State
Buffer

36. Combinational Logic 36
Shifters
 8-input, 8-output shifter
 C=1 => right shift, C=0 => left shift

37. Combinational Logic 37
Study Problem
 Course Book Chapter – 4 Problems
 4 – 31
 Construct a 16x1 multiplexer with two 8x1 and
one 2x1 multiplexer. Use block diagrams

38. Combinational Logic 38
Study Problem
 Course Book Chapter – 4 Problems
 4 – 34
implements
r
multiplexe
hat the
function t
Boolean
the
Determine
'
;
;
1
;
0
inputs
data
The
ly.
respective
S
and
,
S
,
S
inputs
selection
the
to
connected
C
and
B,
A,
inputs
has
r
multiplexe
8x1
An
6
4
0
5
3
7
2
1
0
1
2
D
I
D
I
I
I
I
I
I
I









39. Combinational Logic 39
Study Problems
 Course Book Chapter – 4 Problems
 4 – 1
 4 – 4
 4 – 6
 4 – 11
 4 – 20
 4 – 21
 4 – 25
 4 – 32
 4 – 33
 4 – 35

40. Combinational Logic 40
Questions