Show how a power source, a lamp and a number 23.6 Show that the two circuits (a) and (b) below are...

Question

Show how a power source, a lamp and a number 23.6 Show that the two circuits (a) and (b) below are of switches can be used to represent the following equivalent by drawing truth tables for each circuit. logical functions L=A• B• C L=A+B+C L= (A • B) + (C • D) L=Affi B (b) 23.2 Derive expressions for the following arrangements 23.7 Repeat the operations in Exercise 23.6 for the fol-using AND, OR and NOT operations. lowing circuits.
	
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EXERCISES 589
• In digital electronics, several number systems are used, the most
common being decimal, binary, octal and hexadecimal.
• As binary numbers use only two digits, 0 and 1, arithmetic is simpler
than it is for decimal numbers.
• Although simple binary code is the most frequently used option for
representing numeric information, it is not the only method. In some
applications, the use of other representations, such as Gray code,
may be more appropriate.
• Codes are also used for non-numeric information, such as the ASCII
code, which is used for alphanumeric data.
• Some coding techniques allow error detection and, in some cases,
correction.
Exercises
23.1 Show how a power source, a lamp and a number 23.6 Show that the two circuits (a) and (b) below are
of switches can be used to represent the following equivalent by drawing truth tables for each circuit.
logical functions
L = A · B · C
L = A + B + C
L = (A · B) + (C · D)
L = A ? B
23.2 Derive expressions for the following arrangements
23.7 Repeat the operations in Exercise 23.6 for the fol-
using AND, OR and NOT operations. lowing circuits.
23.8 Simulate the pairs of circuits in Exercises 23.6 and 
23.7 and con?rm that each pair produces the same
output for every possible combination of the inputs.
23.9 List all the possible values of a Boolean constant.
23.10 List all the possible values of a Boolean variable.
23.11 What symbols are used in Boolean algebra to repres-
ent the functions AND, OR, NOT and Exclusive
OR?
23.12 Write the function of a three-input NOR gate as a
Boolean expression.
23.13 Given that A is a Boolean variable, evaluate and
23.3 If the two circuits given in the previous exercise then simplify the following expressions: A ·1; A · a;
were described by truth tables, how many rows 1 + A; A + a; 1 · 0; 1 + 0.
would each table require? 23.14 Exercises 23.6 and 23.7 illustrate fundamental laws
23.4 Sketch the truth table of a three-input NAND gate....

Robert · Accepted Answer

Solution: 
23.4: 
Truth table for 3 input NAND gate is: 
A B C NAND 
0 0 0 1 
0 0 1 1 
0 1 0 1 
0 1 1 1 
1 0 0 1 
1 0 1 1 
1 1 0 1 
1 1 1 0
23.7: 
Truth table for circuit a: 
A  ̅ B  ̅  ̅ ̅ 
0 1 0 1 1 
0 1 1 0 0 
1 0 0 1 0 
1 0 1 0 0
Truth table for circuit b: 
A B        ̅̅ ̅̅ ̅̅ ̅̅   ̅ ̅ 
0 0 0 1 1 
0 1 1 0 0 
1 0 1 0 0 
1 1 1 0 0
Hence the columns are having same output hence they are equivalent. 
23.18 
Truth table is: 
A B C X 
0 0 0 0 
0 0 1 0 
0 1 0 0 
0 1 1 1 
1 0 0 0 
1 0 1 1 
1 1 0 1 
1 1 1 0
Circuit implementation:
23.20
    (   )̅̅ ̅̅ ̅̅ ̅̅ ̅̅  
     ̅  ̅ 
       ̅  ̅ 
    (   ̅)  ̅
23.21 
A/BC  ̅ ̅  ̅  BC   ̅ 
 ̅ 1 1 0 0 
A 1 1 1 0 
A 
B 
A 
C 
B 
C 
X 
   ̅     
AB/CD  ̅ ̅  ̅  CD   ̅ 
 ̅ ̅ 1 1  1 
 ̅   1   
AB 1 1   
  ̅ 1 1
   ̅    ̅   ̅ ̅ ̅ 
23.30 
Truth table for gray code and binary code: 
Decimal Gray code Binary code 
0 000 000 
1 001 001 
2 011 010 
3 010 011 
4 110 100 
5 111 101 
6 101 110 
7 100 111
A 
B 
C 
G 
R 
A 
Y 
C 
O 
D 
E 
B 
I 
N 
A 
R 
Y
23.33 
A de multiplexer converts two input select to 4 data output: 
Input Select Data Output 
L M  
0 0 A 
0 1 B 
1 0 C 
1 1 D
A 
B 
C 
D 
L 
M 
24.11
D1 
D2 
D3 
D4 
D5 
D6 
D7 
D8 
Q1 
Q2 
Q3 
Q4 
Q5 
Q6 
Q7 
Q8 
Clock  
Pulse  
24.16 
24.

Show how a power source, a lamp and a number 23.6 Show that the two circuits (a) and (b) below are of switches can be used to represent the following equivalent by drawing truth tables for each...

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