Download Problem 1

University of the West Indies
Dept. of Electrical and Computer Engineering
ECNG1014/EE19D Digital Electronics
Tutorial 1 (Introduction and Numbers)
Problem 1
1. For the pulse shown in figure 1, graphically determine the following:
(a) rise time, (b) fall time, (c) pulse width, (d) amplitude.
Figure 1
2. Consider the signal V(t) of figure 2.
Figure 2.
a) Determine its period.
b) Determine its duty cycle.
3. Name the logic function of each block in figure 3 based on your observation of
the inputs and outputs.
Figure 3.
4. A pulse waveform with a frequency of 10 kHz is applied to the input of a counter.
During 100 ms, how many pulses are counted? What will be the value in binary of
the output if this counter is a modulo-8 binary counter?
Problem 2.
1. Convert the following numbers with the indicated bases to decimal: (120112)3,
(4332)5, and (AB5)16
2. Convert the following numbers from a given base to the other three bases listed in the
table
Decimal
Binary
Octal
Hexadecimal
345.23
?
?
?
?
1110.111
?
?
?
?
657.234
?
?
?
?
123.A
3. Using the IEEE 754 floating-point standard for 32-bit numbers (single precision),
determine the correct floating-point representation of -15, 1/64, 103. What is the smallest
positive number that can be represented?
4. What are the 8-bit binary representations of 10 and -10?
a) Sign magnitude
b) One’s complement
c) Two’s complement
5. Decode the following ASCII Code:101101011110100
6. Represent the decimal number 675 and 456 in packed BCD
Problem 3 (From the Textbook)
1. Convert the following octal numbers into binary and hexadecimal :
a. (7436.11)8 = (?)2 = (?)16
b. (25352321)8 = (?)2 =(?)16
2. Convert the following hexadecimal numbers into binary and octal:
a. (9E36.7A)16 = (?)2 = (?)8
b. (DEAD.BEEF)16 = (?)2 = (?)8
3. Write the 8-bit signed-magnitude, two’s complement and one’s complement
representations for each decimal number: + 25, + 120, +82, -42, -111.
4. Each of the following arithmetic operation is correct in at least one number
system. Determine possible radices of the numbers in each operation.
a. 1234 + 5432 = 6666
b. 41 / 3 = 13
c. 23 + 44 + 14 +32 = 223
Problem 4
1. The solution to the quadratic equation x2 -11x + 22 = 0 is x = 3 and x = 6. What is
the base of the numbers?
2. Using the IEEE 754 floating-point standard for 32-bit numbers, determine the
correct floating-point representation for + 2.5, - 2.5, 106 and 1/256
3. There is a 64-bit version of the IEEE 754 floating-point format that employs a
sign bit s, an 11-bit exponent E, and a 52-bit mantissa M. Normal numbers are
given by the formula N = (-1)s2E-1023(1.M), where 0 < E < 2047. Determine the
largest and smallest positive (nonzero) numbers that are representable in this
format, giving your answers as 16-bit digit hexadecimal strings.