1. Show a truth table for a 1-bit full subtractor that has a borrow input bin and inputs x and y, and produces a difference, d, and a borrow
output, bout.
bin
x - y/bout d
2. Show truth tables for each of the following.
A. There are four inputs and three outputs. The inputs, w, x, y, z,
are codes for the grade that may be received:
0000 A 0100 B2 1000 D1 1100 Incomplete
0001 A2 0101 C1 1001 D 1101 Satisfactory
0010 B1 0110 C 1010 D2 1110 Unsatisfactory
0011 B 0111 C2 1011 F 1111 Pas
The outputs are
1: a 1 if and only if the grade is C or better (only letter grades; C2 is not C or better)
2: a 1 if and only if the university will count it toward the 120 credits required for a degree (passing grade only).
3: a 1 if and only if it will be counted in d icomputing a grade point average (letter grades only).
B. This system has four inputs and three outputs. The ®rst two inputs, a and b, represent a 2-bit binary number (range of 0 to 3). A second binary number (same range) is represented by the other two inputs, c and d. The output f is to be 1 if and only if the two numbers differ by exactly 2. Output g is to be 1 if and only if the numbers are equal. Output h is to be 1 if and only if the second number is larger than the ®rst.
C. The system has four inputs. The ®rst two, a and b, represent a number in the range 1 to 3 (0 is not used). The other two, c and d, represent a second number in the same range. The output, y, is to be 1 if and only if the ®rst number is greater than the second or the second is 2 greater than the ®rst.
D. A system has one output, F, and four inputs, where the ®rst two inputs (A, B) represent one 2 bit binary number (in the range 0 to 3) and the second two inputs (C, D) represent another binary number (same range). F is to be 1 if and only if the two numbers are equal or if they differ by exactly 1.
E. A system has one output, F, and four inputs, where the ®rst two inputs (A, B) represent one 2-bit binary number (in the range 0 to 3) and the second two inputs (C, D) represent another binary number (same range). F is to be 1 if and only if the sum of the two numbers is odd.
F. The system has four inputs. The ®rst two, a and b, represent a number in the range 0 to 2 (3
is not used). The other two, c and d, represent a second number in the same range. The output, y, is to be 1 if and only if the two numbers do not differ by more than 1.
G. The months of the year are coded in four variables, abcd, such that January is 0000, February is 0001, . . . , and December is 1011. The remaining 4 combinations are never used. (Remember: 30 days has September, April, June, and November. All the rest have 31, except February. . . .). Show a truth table for a function, g, that is 1 if the month has 31 days and 0 if it does not.
H. The months of the year are coded as in 2g, except that February of a leap year is coded as 1100. Show a truth table with ®ve outputs, v, w, x, y, z that indicates the number of days in the selected month.
I. Repeat 2h, except that the outputs are to be in BCD (8421 code). There are now six outputs, u, v, w, x, y, z (where the ®rst decimal digit is coded 0, 0, u, v and the second digit is coded w, x, y, z).
J. The system has four inputs, a, b, c, and d, and one output, f. The last three inputs (b, c, d) represent a binary number, n, in the range 0 to 7; however, the input 0 never occurs. The ®rst input (a) speci®es which of two computations is made. a 5 0: f is 1 iff n is a multiple of 2 a 5 1: f is 1 iff n is a multiple of 3
K. The system has four inputs, a, b, c, and d, and one output, f. The ®rst two inputs (a, b) represent one binary number (in the range 0 to 3) and the last two (c, d) represent another number in the range 1 to 3 (0 never occurs). The output, f, is to be 1 if the second number is at least two larger than the ®rst.
L. Show the truth table for a system with four inputs, a, b, c, and d, and two outputs, f and g. The inputs represent a BCD digit between 1 and 9 (8421 code). All other inputs never happen. The output f is 1 if and only if the input represents an odd number larger than 6 or an even number less than 7. The output g is 1 iff the input represents a perfect square. (A perfect square is a number whose square root is an integer).