Consider a ternary, normalized floating-point number system that is base 3. Anal
ID: 3879754 • Letter: C
Question
Consider a ternary, normalized floating-point number system that is base 3. Analogous to a bit, a ternary digit is a trit. Assume that a hypothetical ternary computer uses the following floating-point representation: where sm is the sign of the mantissa and se is the sign of the exponent (0 for positive, 1 for negative), t1, t2, t3 and t4 are the trits of the mantissa, and e1, e2 are the trits of the exponent, where each trit is 0,1 or 2. For parts (a) to (b), Xio) is used to indicate that the number provided is in decimal. Show all your work for all parts.Explanation / Answer
Answer:
(9)10 = (0100)3 and (27)10 = (1000)3
The exponent for both the numbers are (0)10 = (00)3
Thus in ternary floating point representation,
(9)10 = 0 0 0100 00
(27)10 = 0 0 1000 00
In floating point representation, 2 consecutive numbers generally have the same exponent while the difference between mantissas is 1.
Therefore the next real number of (9)10 has the following ternary floating point representation:
0 0 0101 00 = (10)10 having the difference of 1(10-9)
Also, the previous real number of (27)10 has the following ternary floating point representation:
0 0 0222 00 = (26)10 having the difference of 1(27-26)
Similarly, it can be shown that the gap between 2 consecutive numbers in the interval (9)10 and (27)10 is (1)10.
NB: Hope it helps. Let me know any concern.