Chapter 4: Q43E (page 273)
Use the extended Euclidean algorithm to express gcd(144,89) as a linear combination of 144 and 89.
gcd(144,89) = 1
Linear combinations
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35. What integer does each of the following one’s complement representations of length five represent?
a) 11001 b) 01101 c) 10001 d) 11111
a) Define the greatest common divisor of two integers.
b) Describe at least three different ways to find the greatest common divisor of two integers. When does each method work best?
c) Find the greatest common divisor of .
d) Find the greatest common divisor of .
Give a procedure for converting from the hexadecimal expansion of an integer to its octal expansion using binary notation as an intermediate step.
32. Show that a positive integer is divisible by 11 if and only if the difference of the sum of its decimal digits in even- numbered positions and the sum of its decimal digits in odd-numbered positions is divisible by 11.
a) Explain why ndiv 7 equals the number of complete weeks in days.
b) Explain why n div 24 equals the number of complete days inn hours.
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