662
Boolean Algebra and Computer Logic
34. The space shuttle was controlled by three on-board computers; binary output from these three computers
was compared and a majority vote was required for certain actions to take place. Find a truth function, a
Boolean expression, and a logic network that outputs the majority vote of the three input values.
35. You have just been hired at Mercenary Motors. Your job is to design a logic network so that a car can be
started only when the automatic transmission is in neutral or park and the driver’s seat belt is fastened.
Find a truth function, a Boolean expression, and a logic network. (There is a don’t-care condition to the
truth function, since the car cannot be in both neutral and park.)
36. Mercenary Motors has expanded into the calculator business. You need to design the circuitry for the
display readout on a new calculator. This design involves a two-step process.
a. Any digit 0, 1, … , 9 put into the calculator is first converted to binary form. Part (a) of the accompanying figure illustrates this conversion, which involves four separate networks, one each for x 1 to x 4 . Each
network has 10 inputs, but only 1 input can be on at any given moment. Write a Boolean expression and
then draw a network for x 2 .
b. The binary form of the digit is then converted into a visual display by activating a pattern of seven outputs arranged as shown in figure (b). To display the digit 3, for example, y 1 , y 2 , y 3 , y 5 , and y 7 must be
on, as in figure (c). Thus, the second step of the process can be represented by figure (d), which involves
seven separate networks, one each for y 1 to y 7 , each with four inputs, x 1 to x 4 . Write a truth function, a
Boolean expression, and a network for y 5 and for y 6 .
0
1
2
3
4
5
6
7
8
9
y 1
x 4 x 3 x 2 x 1
x 4 x 3 x 2 x 1
y 2
y 3
y 4
y 5
y 6
y 7
Logic
for
binary
encoder
Logic
for
display
readout
(d)
(c)
(b)
(a)
y 6
y 7
y 3
y 2
y 1
y 4
y 5