Consider the following signal encoding technique. Binary data are presented as input, am for m= 1,2,3,...Two levels of processing occur. First, a new set of binary numbers are produced: Bo=0 bm = (am + bm-1)mod 2 These are then encoded as Cm = bm - bm-1 On reception, the original data are recovered by: %3D am = Cm mod 2 a. Verify that the received values of equal the transmitted values of am. b. What sort of encoding is this?

Problem 6: In a binary phase shift keying (BPSK) communications system, one of two equally probable bits, 0 or 1, is transmitted every T seconds. If the kth bit is je {0,1}, the waveform ;(t) = cos(27 fot + jr) is trans- mitted over the interval [(k- 1)T, kT). Let X(t) denote the random process in which two symbols are transmitted in the interval (0, 27, and let fo = 2/T. %3D Sketch the sample space and corresponding sample functions of the process X (t).

Design the most efficient (fastest) implementation for a 3-to-8 binary decoder. Determine the “cost” and worst-case delay of your design.

Consider this 1-bit ALU design, as shown in class (note that the rounded rectangles controlled by Ainvert, Binvert, and Operation represent multiplexers):     If I want Result to be the result of a - b, then what value do each of these other inputs need to be?     Ainvert : 0 or 1   Binvert : 1 or 0   CarryIn: 1 or 0   Operation : 00 , 01, 10, 11 which one ?

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The symbol £ is magnified and shown in Figure 1 with a grid superimposed. Figure 1 The image in Figure 1 is to be encoded and encrypted using the following steps: 1. Each of the five horizontal rows of the picture is encoded as a 5-bit binary number. White squares are encoded as Os and black squares as 1s. The horizontal rows are therefore encoded as: Row 1: 00110 Row 2: 01001 Row 3: 11100 Row 4: 01000 Row 5: 11110 2. Starting from the left, the first binary digit is multiplied by 16, the second by 8, the third by 4, the fourth by 2, and the fifth by 1. This will convert the 5-bit binary numbers to decimal numbers as shown below: Row 1: (0 x 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 0 + 0 +4+2+0 = 6. Row 2: (0 x 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1) = 0 + 8 +0+0+1 = 9. Row 3: (1 x 16) + (1 × 8) + (1 × 4) + (0 × 2) + (0 × 1) = 16+8+4 + 0 + 0 = 28. Row 4: (0 x 16) + (1 × 8) + (0 × 4) + (0 × 2) + (0 × 1) = 0 + 8 +0+0+0= 8. Row 5: (1 x 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1)…

Consider a hypothetical 8 bit floating point machine representation with a sign bit, a 3 bit exponent, and a 4 bit mantissa (se1e2e3b1b2b3b4), where the exponent bias is 3 (add 3 to exponent of number to form machine representation). Recall that actual mantissa has 5 bits, since the leading 1 is not stored on the machine. (a) What is the number ?≈2.718 in this 8-bit format? (b) What is the number that (10100111)2 represents in this 8-bit format? (c) What is the upper bound of the relative error when representing a real number in this 8-bit format?

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Data communication subject

b. Assuming the starting voltage level 'high' (positive voltage) and data stream is '11010101', draw the two waveforms of the encoded voltage levels based on these conditions. Perform Polar NRZ-I and Polar RZ encoding schemes. Discuss the difference in terms of common characteristics betwveen these two line coding schemes.