1
NAME _______________________________________
EXAM 1: SPRING 2022
THERE ARE 12 QUESTIONS ON THIS EXAMINATION. ANSWER ALL QUESTIONS.
THE EXAM IS 108 POINTS. YOU MAY USE A CALCULATOR AND BOOLEAN LAWS SHEET. SUBMIT ONE PDF FILE IN CANVAS.
1) (2 pts. each) Define the following terms in 1-2 sentences.
a) fallacy: _____________________________________________________________
____________________________________________________________________________
) essential prime implicant:
____________________________________________________________________________
____________________________________________________________________________
c) ASCII: _____________________________________________________________
____________________________________________________________________________
2) (4 pts. each) Perform the following conversions:
a) Convert XXXXXXXXXXto hexadecimal.
) Convert D74E958316 to binary.
c) 6ABF16 to decimal.
3a) (2 pts. each) Represent the decimal number -89 in binary using 8-bit:
i. Signed magnitude: ____________________________
ii. One's complement: ____________________________
iii. Two's complement: ___________________________
3b) (2 pts. each) What decimal value does the 8-bit binary number XXXXXXXXXXhave if:
i. it is interpreted as an unsigned number? ___________________________
ii. it is on a computer using signed-magnitude representation? _______________________
iii. it is on a computer using one’s complement representation? _______________________
iv. it is on a computer using two’s complement representation? _______________________
4) (5 pts. each) Perform the 8-bit 2’s complement binary operation. Indicate the result and whether there is overflow or not.
a XXXXXXXXXX
4b) Perform the 2’s complement hexadecimal operation. Assume all numbers are 32 bits. Indicate the result and whether there is overflow or not. If the result is negative, show the hex value with the negative sign.
7ADEFDE2
- EBED9328_
4c) Perform the following binary multiplication. Assume that all values are signed 2’s complement numbers.
XXXXXXXXXX
* 1101
5) (5 pts.) Perform the following binary division. Assume that all values are unsigned numbers.
XXXXXXXXXX/1101
6a) (6 pts. each) Find the decimal represented by the 32-bit single precision floating point number for the hexadecimal value C47CD000.
6b) Convert the decimal real number XXXXXXXXXXto a binary floating point value.
7) (5 pts.) Construct a truth table for the following Boolean function:
xyz + x(yz)' + x'(y+z) + (xyz)'
8a) (6 pts.) Simplify the following functional expression using Boolean alge
a and its identities. List the identity used at each step.
F(x,y,z) = (x' + y + z')' + xy'z' + yz + xyz
8b) (3 pts. each) Given the following truth table:
i) Write the function as a canonical sum of products:
ii) Write the function as a canonical product of sums.
9) (5 pts.) Write an expression for the complement of F if F(x,y,z) = (x'+y)(x+z)(y'+z)'.
10a) (5 pts.)
Write the simplified expression for the Boolean function defined by the following K-map, which uses “don’t cares”.
Simplifies to:
(1 pt. each)
10b) Identify the distinguished 1-cells with a “*” in the K-map. How many are there? ________
10c) How many Essential Prime Implicants in the K-map? ________
11a) (8 pts.)
Create the K-map and then simplify for the following function (leave in sum-of-products form):
F(w,x,y,z) = y'z + wy' + w'xy + w'x'yz' + wx'yz'
Simplifies to:
(1 pt. each)
11b) Identify the distinguished 1-cells with a “*” in the K-map. How many are there? ________
11c) How many Essential Prime Implicants in the K-map? ________
SHORT ANSWERS:
12a) (1 pt.) Suppose we are given the following subset of binary words, created for a 7-bit memory word with one parity bit: XXXXXXXXXX, XXXXXXXXXX, XXXXXXXXXX, and XXXXXXXXXXDoes this code use even or odd parity? Explain in 1-2 sentences.
12b) (1 pt.) If you were going to write a program to convert uppercase ASCII characters to lowercase, what algorithm would you use to accomplish the conversion? Explain in 1-2 sentences.
12c) (1 pt. each) Example: Let F(A,B,C) = Σm(0, 1, 2, 6) and G(A,B,C)=Σm(1, 3, 5, 6, 7)
Find the following minterms using the operations on the functions:
F + G = ________________________
F G = ________________________
F’ G = ________________________
END OF EXAM
EXTRA SHEET