Chapter 3 - Pages 106-111 - Due:
Wednesday, October 11.
Chapter 3: 1,
2, 3 b,d, 4 a,c,d, 10, 12, 26, 27. (Points: 4,
4, 4, 6, 4, 3, 6, 4)
Notes on the book's
notation: The book sometimes uses "minterms" and
"maxterms" to express
Boolean formulas. Minterms are products of Boolean
variables and maxterms are sums. Pages 46-50 of your
book explains the notation. The sum of products is Sigma
of minterms, and the
product of sums is Pi of maxterms. If
you don't understand the "Sigma" and "Pi" notation please
Problem: (5 points)
Design a circuit for
this problem. There are many ways to do this, from
sheer brute force, to methods that use circuits we discussed
including adders and multiplexers.
Given a 4-bit number
x, output a BCD
number (4 bits) equal to the units digit of x in base 10, and
light up a "tens digit" single LED whenever the value of x is between 10 and 15
inclusive. For example: if x = 1101 (13 in base 10), then the "tens"
LED will be lit (1). And the BCD units digit will be
0011 (3 in base 10).
The idea is that you want to display a two digit number, the right digit is 7-segment display fed by a 4-bit BCD number, and the left digit is either 0 or 1, so it is represented by a single LED. You do not need to design or draw the circuit to take the 4-bit BCD number and output the 7-segment display. That circuit is in the book and not part of your problem. Your part of the job is to take 4-bits and output 5 bits: 1 for the ten's digit LCD, and 4 for the BCD units digit.