Fixed-point number representation Consider a fixed-point, radix-3 number system,
ID: 2079598 • Letter: F
Question
Fixed-point number representation Consider a fixed-point, radix-3 number system, using the digit set [-1, 1], in which numbers are represented with k integer digits and l, fractional digits as: d_k - 1 d_k - 2 ... d_1d_0.d_-1d_-2...d_-l Determine the range of numbers represented as a function of k and l. Given that each radix-3 digit needs a 2-bit encoding, compute the representation efficiency of this number system relative to the binary representation. Outline a carry-free procedure for converting one of the above radix-3 numbers to an equivalent radix-3 number using the redundant digit set [0, 3]. By a carry-free procedure, we mean a procedure that determines each digit of the new representation locally from a few neighboring digits of the original representation, so that the speed of the circuit is independent of the length of the original number.Explanation / Answer
If the number system is radix-3 number system, then in the number system there are only three digits: 0 1 and 2.
So, the maximum number that can be represented by this scheme is (222.222)3 and the minimum number is (000.000)3
For the sake of understanding, let's explain the number (222.222)2=2X32+2X31+2X30+2X3-1+2X3-2+2X3-3=26.963 in decimal system.
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