P7.52 Applying De Morgan’s Laws to the output of the circuit, we have
P7.53* The truth table is:
A B A
B
0 0 0
Thus, we can write the product of sums expression and apply De Morgan’s
Laws to obtain:
The circuit is:
P7.54 The truth table is:
A B A
B
0 0 0
The circuit is:
P7.55 An example of a decoder is a circuit that uses a BCD input to produce the
logic signals needed to drive the elements of a seven-segment display.
P7.56* (a)
S
1
S
2
ST
E
0 0 0 0
0 0 1 1
(c) Circuit diagram:
P7.57 (a) The truth table is:
B E F G I
0 0 0 0 0
0 0 0 1 0
P7.58 The truth table (x = don’t cares) is:
B
8
B
4
B2
B
1
A B C D
0 0 0 0 1 1 1 1
0 0 0 1 0 1 1 0
P7.59* (a) The Karnaugh map is:
(c) Inverting the map, and writing the minimum SOP expression yields
P7.60 (a) The Karnaugh map is:
(c) Inverting the map, and writing the minimum SOP expression yields two
possibilities:
P7.61 (a) The Karnaugh map is:
(c) Inverting the map, and writing the minimum SOP expression yields
P7.62 (a) The Karnaugh map for
D
is:
P7.63 (a) The Karnaugh map is:
(b)
BCABD
P7.64 (a) The Karnaugh map is:
(c) The circuit is:
(d) Inverting the map, and writing the minimum SOP expression
P7.65* (a) The Karnaugh map is:
(c) The circuit is:
P7.66 (a) The Karnaugh map is:
(c) The circuit is:
P7.67 (a) The Karnaugh map is:
(c) The circuit is:
P7.68 (a) The Karnaugh map is:
(c) The circuit is:
P7.69 (a) The Karnaugh map is:
(c) The circuit is:
(d) Inverting the map, and writing the minimum SOP expression yields
P7.70 The Karnaugh map (with the decimal equivalent of each word in the upper
right hand corner of each square) is:
By inspection, the minimal SOP expression is:
P7.71 The Karnaugh map (with the decimal equivalent of each word in the upper
right hand corner of each square) is:
P7.72 The truth table is:
S
I
1
I
2
O
1
O
2
0 0 0 0 0
The Karnaugh maps are:
The logic circuit is:
P7.73 The Karnaugh map (with the hexadecimal equivalent of each word in the
upper right hand corner of each square) is:
By inspection the minimal SOP expression is:
P7.74 The Karnaugh map for a three-member council is:
By inspection, we see that three two-cubes are needed and the minimal
SOP expression is
For a five-member council, the Karnaugh map consists of two four-
P7.75 The Karnaugh map is
P7.76 (a) The truth table for the circuit of Figure P7.76 is
A
B C
D
P
0 0 0 0 0
0 0 0 1 1
1 0 0 1 0
(b) The Karnaugh map for
P
is:
(c) The parity check can be performed by the same method as used in
Figure P7.76, namely to XOR all of the bits. The circuit is:
P7.77 By inspection, we see that
The Karnaugh maps for
Y
and
Z
are: