Chapter 4: Q40E (page 273)
Using the method followed in Example 17, express the greatest common divisor of each of these pairs of integers as a linear combination of these integers.
a) 9,11 b) 33,44 c) 35,78 d) 21,55 e) 101,203 f)124,323 g) 2002,2339 h) 3457,4669 i) 10001,13422
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Show that is an irrational number. Recall that an irrational number is a real number that cannot be written as the ratio of two integers.
a) Define what it means for a and b to be congruent m odulo 7.
b) Which pairs of the integers-11,-8,-7,-1,0,3 and 17are congruent ?
c) Show that ifa and bare congruent m odulo 7, then 10a+13 and -4b+20 are also congruent m odulo 7.
Find
Answer Exercise 37 for two's complement expansion.
How is the one's complement representation of the sum of two integers obtained from the one's complement representations of these integers?
It can be shown that every integer can be uniquely represented in the form
where, or 1 for j=0,1,2, …., k. Expansions of this type are called balanced ternary expansions. Find the balanced ternary expansions of
a) 5 .
b) 13 .
c) 37 .
d) 79 .
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