Exam 2013

Question 1

From a Karnaugh diagram the result can be:

a. More than one expression representing a minimal sum of products
b. Only one expression representing the minimal sum of products
c. Two expressions, each representing a minimal sum of products, but only if
one or several “don’t cares” appear in the map
d. None of the above

Answer 1

a -> K-maps can result in more than one expression representing a minimal sum of products

Question 2

How many of the following statements are true?
 0000 0010 10102 = 528 = 4210 = 3A16
 0000 1000 00002 = 2008 = 12810 = 8116
 0011 1111 10002 = 17708 = 101610 = 3F816
 0100 0000 00002 = 20018 = 102410 = 40016
 1000 0000 00002 = 40008 = 204910 = 80016

(ATTN: The notation 1238 means: the value 123 in octal representation.)

a. 1
b. 2
c. 3
d. 4

Answer 2

a -> False statements:

1st: hexadecimal should be 2A
2nd: hexadecimal should be 80
4th: octal should be 2000
5th: decimal should be 2048

Question 3

What are the 8-bit binary 2’s Complement representations of –910 and 910?

a. 1111 0110 and 0000 1001
b. 1111 0111 and 0000 1001
c. 1111 0110 and 0000 1001
d. 1111 0111 and 0000 1001

Answer 3

d ->
$9_{10}$ → 0000 1001

$-9_{10}$ → 1111 0110 + 0000 0001 = 1111 0111

Question 4

Consider the multiplication of the following two numbers represented in 8-bit
2’s Complement:
0111 0011
0000 1111

What is the minimal number of addition/subtraction operations to perform this
multiplication?

Answer 4

4 operations needed since there are 4x 1s

No operations are performed for the 4x 0s

Question 5

A two-digit octal number is erroneously interpreted as a decimal number, and thus its value larger by 12 (decimal) units. How much larger would the value have been if the number would have been erroneously interpreted as a hexadecimal number?

a. 16
b. 24
c. 32
d. 48

Answer 5

d -> Number xy

Octal: 8x + y

Decimal: 10x + y

Hexadecimal: 16x + y

Difference between decimal and octal → 2x = 12 → x = 6

Difference between hexadecimal and octal → 8x = 8(6) = 48

Question 6

An integer is represented in binary-coded decimal representation (BCD), as a
sequence of characters in ASCII code derived from the decimal representation of the integer (ASC), and in binary code (BIN). What is the correct order, from more to
fewer bits in the representation?
a. ASC, BCD, BIN
b. ASC, BIN, BCD
c. BCD, ASC, BIN
d. BCD, BIN, ASC

Answer 6

a ->
Binary-coded decimal (BCD): 32
ASCII code (ASC): thirty-two
Binary code (BIN): 0010 0000

Question 7

S = 1 11111111 00000000000000000000000

is a number in IEEE754 floating point representation

What is the value of S?

a. -∞
b. 2
- 149
c. 2
- 126
d. NaN

Answer 7

a -> Positive and negative infinity:

x 11111111 00000000000000000000000

Sign = 0 for positive infinity, 1 for negative infinity

Exponent = all 1 bits

Mantissa = all 0 bits

NaN:

x 11111111 xxxxxxxxxxxxxxxxxxxxxxx

Sign = 0 or 1

Exponent = all 1 bits

Mantissa = anything but all 0 bits (would represent infinity in that case)