1. The Digital Logic Level
College of Computer and Information Sciences,
Majmaah University, AlMajmaah
Chapter 5
The Digital Logic Level
Dr. Mohsen NASRI
Merci Mr le président
Mr. Les membres de jury;
Je commencerai cette présentation en vs souhaitant la bienvenue à l’occasion de la conclusion de mes travaux sur les approches….sujet principale de cette setenance.
College of Computer and Information Sciences,
Majmaah University, Al Majmaah

2. Gates and Boolean Algebra
Logic Gate
Truth Table
AND OR
NOT
A B Y
A B Y
A Y
0 1
1 0
NAND
A B Y
NOR
A B Y

3. Gates and Boolean Algebra1 A 1 A 1 A A A
0 dominates in AND
0 blocks the output
1 passes signal A
1 dominates in OR
1 blocks the output
0 passes signal A
Identity A * 1 = A A + 1 = 1
A * 0 = A + 0 = A
Complement A + A’ = A * A’ = 0

4. Gates and Boolean Algebra Cont…
Distributive Law
A(B+C) = AB + AC
A+BC = (A+B)(A+C) A B A B C A C A B A B C A C
Associativity
(A+B) + C = A + (B+C) C A A B B C

5. Gates and Boolean Algebra Cont…
Associativity
(AB)C = A(BC) C A A B B C
DeMorgan’s Law (A+B)’ = A’B’ (AB)’ = A’ + B’
Consensus Theorem AC + AB + BC’ = AC + BC’

6. Circuit Equivalence
Construction of (a) NOT, (b) AND, and (c) OR gates using only NAND gates or only NOR gates.

7. Circuit Equivalence Cont…
Two equivalent functions (a) AB + AC, (b) A(B + C).

8. Circuit Equivalence Cont…
Some identities of Boolean algebra.

9. Circuit Equivalence Cont…
Alternative symbols for some gates: (a) NAND, (b) NOR, (c) AND, (d) OR

10. Circuit Equivalence Cont..
(a) The truth table for the XOR function.
(b-d) Three circuits for computing it.

11. An SSI chip containing four gates.
Integrated Circuits
An SSI chip containing four gates.
Tanenbaum, Structured Computer Organization, Fifth Edition, (c) 2006 Pearson Education, Inc. All rights reserved

12. Multiplexers
A multiplexer can use selecting bits to choose one of several input bits to be the output.
A selector chooses a single data input and passes it to the MUX output
It has one output selected at a time.
Consists of:
2n Inputs
Output (single)
n Selectors (depends on # of inputs)

13. Multiplexers examples
2 to 1 line multiplexer d S
Truth table S d a 1 b
4 to 1 line multiplexer
Truth table a b S c d
Sel1
MSB
Sel1
Sel0
LSB

14. Multiplexers examples
8 to 1 line multiplexer
Truth table B A C D0 D1 D2 D3 D4 D5 D6 D7 F F A B C D0 D1 1 D2 D3 D4 D5 D6 D7

15. Multiplexers Examples
8 to 1 line multiplexer B A C D0 D1 D2 D3 D4 D5 D6 D7 F

16. A demultiplexer connects the data input to the selected output.
Demultiplexers
A demultiplexer connects the data input to the selected output.
A selector chooses one of the multiple data input and passes it to the single output
It has one intput selected at a time.
Consists of:
One Input
2n Output
n Selectors (depends on # of inputs)

17. Demultiplexers Examples
1 to 4 Demultiplexer
Truth table
Out0 In S1 S0 I A B
Out1
Out2
Out3 A B D0 D1 D2 D3 I 1 D0 D1 D2 D3

18. Demultiplexers Examples
1 to 4 Demultiplexer I D0 D1 D2 D3
Out0 In S1 S0 I A B
Out1
Out2
Out3 D0 D1 D2 D3

19. A decoder converts input code words into output code words.
A decoder chooses one of the multiple data input by decoding the binary value on the inputs.
Consists of:
n Inputs
2n Output

20. Decoder Examples 2 to 4 Decoder circuit B A I0 I1 Out0 Out1 Out2 Out3
msb
Truth table A B D0 D1 D2 D3 1

21. Decoder Examples Cont…
2 to 4 Decoder circuit B A D0 D1 D2 D3 B I0 I1 A
Out0
Out1
Out2
Out3 D0 D1 D2 D3

22. Decoder Examples Cont…
3 to 8 Decoder circuit
Truth table C I0 I1 B
Out0
Out1
Out2
Out3 D0 D1 D2 D3 A D4 D5 D6 D7 I2
Out4
Out5
Out6
Out7 D7 D6 D5 D4 D3 D2 D1 D0 C B A 1

23. Decoder Examples Cont…
3 to 8 Decoder circuit C I0 I1 B
Out0
Out1
Out2
Out3 D0 D1 D2 D3 A D4 D5 D6 D7 I2
Out4
Out5
Out6
Out7

24. Adders
Half adder
Truth table
(b)

25. Adders Cont…
1-bit Adder

26. Arithmetic Logic Units
A 1-bit ALU.

27. Concours Assistanat Session 2008
Thank you
Have a nice day
Juillet 2008
Concours Assistanat Session 2008