Write (a) 29 in the binary notation, (b) write 29 in tertiary notation. (Answers only, no need to justify. Hint: Use the algorithm given in the proof of Proposition 12.1. Make sure you got correct answer by verifying the equation of Proposition 12.1.)

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Write (a) 29 in the binary notation, (b) write 29
in tertiary notation.
(Answers only, no need to justify. Hint: Use the
algorithm given in the proof of Proposition
12.1. Make sure you got correct answer by
verifying the equation of Proposition 12.1.)
Transcribed Image Text:Write (a) 29 in the binary notation, (b) write 29 in tertiary notation. (Answers only, no need to justify. Hint: Use the algorithm given in the proof of Proposition 12.1. Make sure you got correct answer by verifying the equation of Proposition 12.1.)
Proposition 12.1. Let a € N. Let go be the integral quotient of a by
10 and let bo be the remainder of that division. Define q1, 92, ... and
b1, b2, recursively as follows: qi+1 is the integral quotient of qi by
10 and b+1 is the remainder of that division. Let qn be the first zero
number in this sequence. Then
(1) a = b₂10n+bn−110n−1 +...+b210² + b₁10+ bo-
(2) bo, ,bn are the only possible digits for which the above equation
holds.
A sequence of digits bnb-1...b₁bo (as above) is called a decimal no-
tation for a.
Proof. Proof in class.
Note that "n" in the proposition above is the largest natural number
such that 10" <a.
Transcribed Image Text:Proposition 12.1. Let a € N. Let go be the integral quotient of a by 10 and let bo be the remainder of that division. Define q1, 92, ... and b1, b2, recursively as follows: qi+1 is the integral quotient of qi by 10 and b+1 is the remainder of that division. Let qn be the first zero number in this sequence. Then (1) a = b₂10n+bn−110n−1 +...+b210² + b₁10+ bo- (2) bo, ,bn are the only possible digits for which the above equation holds. A sequence of digits bnb-1...b₁bo (as above) is called a decimal no- tation for a. Proof. Proof in class. Note that "n" in the proposition above is the largest natural number such that 10" <a.
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