Page 104 - Engineering Digital Design

PROBLEMS 75

2.21 Use the direct quadratic convergence method to obtain the quotient for the following
fractions. To do this, use Eqs. (2.26) and (2.27).
5
(a) (0.25 -^ 0.75)io in decimal. Find Q after three iterations and rounded to 10~ .
8
(b) (0.01 -^ 0.11)2 in binary. Compare Q after two iterations rounded to 2~ with Q
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after three iterations rounded to 2~ . For comparison, use decimal values derived
from the binary results.
2.22 Carry out the following hexadecimal operations and verify in decimal:
(a) 1A8 + 67B
(b) ACEF1 + 16B7D
(c) 1273i 6-3A8
(d) 89 16 x 1A3
(e) A2 x 15BE3
(f) 1EC87 -T- A5 (Hint: Use decimal *> hex methods with Table P2.3.)

2.23 Convert the following decimal numbers to BCD with the MSDs null (0000), then
carry out the indicated arithmetic in BCD by using Algorithms 2.14 and 2.15 in
Subsection 2.9.6:
(a) 049,0 + 078,0
(b) 168.6,0 + 057.5,0
(c) 093,0-067,0
(d) 034.79,o-156.23,o

2.24 Perform the FPN arithmetic indicated below. To do this follow the examples in Sub-
section 2.9.7.
(a) 135.25,0 + 54.625,0
(b) 54.625,0 - 135.25,o
(c) 3.75,o x 5.0625,0
(d) 4.50,0 x (-2.3125,o)
(e) 6.25 H-(-0.37510)
Note: Use the sign-magnitude FPN system for parts (d) and (e) following Exam-
ples 2.36 and 2.37.
2.25 To add XS3 numbers, a correction by either adding or subtracting 0011 is necessary
depending on whether or not a 1 carry is generated. Study, then write an algorithm
for the addition in XS3 numbers.
2.26 Prove that a self-complementing unit-distance code is not possible.

2.27 An inspection of the binary and Gray codes in Tables 2.1 and 2.12 indicates a unique
relationship between these codes. Examine these codes and devise a simple algorithm
that will permit direct "pencil-and-paper" conversion between them, binary-to-Gray
or vice versa.
2.28 Decipher the following ASCII code. It is given in hexadecimal, MSD first.

57 68 61 74 69 73 79 6F 75 72 6E 61 6D 65 3F