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Unformatted text preview: si,1 = si + x0iyiei mi = si,1 xi + s0i,1yi Solutions Manual  Introduction to Digital Design  February 22, 1999 129 NOTBCD x Y OR y MIN Mem. Cells CLK Figure 8.9: Network for Exercise 8.9 e4 = 1 s4 = 0
The nal gate network for the system is shown in Figure 8.10. : To implement a sequential network that performs a BinarytoGray code conversion we use the given equation: gi = bi bi+1, i = 1; ::::; n , 1 gn = bn Thus, the conversion is done from left to right, storing a new binarycode bit in each clock cycle. Initially the internal variable is 0 bi+1 = 0. The sequential network is shown in Figure 8.11.
Exercise 8.10 To perform subtraction it is necessary to have a representation of negative integers, since the result can be negative. Several of these representations are given in Chapter 10. Here we simplify the problem by assuming that the result is positive. Given two nbit integers represented in the binary number system by x = xn,1 ; : : : ; x0 and y = yn,1 ; : : : ; y0 , and the result represented by sn,1 ; : : : ; s0 , the function to be performed serially in each bit position, for addition and subtraction, is described by the following tables: Exercise 8.11 xi yi ci ci+1 si
0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 Addition xi yi bi bi+1
0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 Subtraction si
0 1 1 0 1 0 0 1 130 Solutions Manual  Introduction to Digital Design  February 22, 1999 x3 x2 x3 x1 y3 y2 y3 y1 1 x3 y3 x y 0 MIN slice NOTBCD ei si
m y3 e i1
x2 y2 x1 y1 x0 y0 s i1
MIN slice MIN slice MIN slice CLK y2 y1 y0 Figure 8.10: Minimum detector for Exercise 8.9 where ci is the carryin bit at position i, and bi is the borrowin bit. Let the variable k indicate the operation to be performed as follows: k= 1 for x + y 0 for x , y Since we want to combine both operations in the same module, let us make c = b. A switching expression for the result si is: si = xi xi ci for i = 1; : : : ; n , 1 sn = cn
BINARYtoGRAY b bi CLK D Q i+1 g i Figure 8.11...
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This note was uploaded on 03/26/2010 for the course CS 187154200 taught by Professor Ercegovac,m.d. during the Winter '09 term at UCLA.
 Winter '09
 Ercegovac,M.D.

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