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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.