Consider the linear arrays AAA[5:50],BBB[-5:10] and CCC[1:8]

Consider the linear arrays: AAA[5:50], BBB[-5:10], and CCC[1:18].

(a) Find the number of elements in each array.

(b) Given Base(AAA) = 300 and w = 4 words per memory cell for AAA, find the addresses of AAA[15], AAA[35], and AAA[55].

Solution

(a) Number of Elements in Each Array

The formula to calculate the number of elements in an array is:

Length = Upper Bound - Lower Bound + 1

For AAA[5:50]:

 Solution:
 Lower Bound = 5, Upper Bound = 50
 Length(AAA) = 50 - 5 + 1 = 46 elements

For BBB[-5:10]:

 Solution:
 Lower Bound = -5, Upper Bound = 10
 Length(BBB) = 10 - (-5) + 1 = 10 + 5 + 1 = 16 elements

For CCC[1:18]:

 Solution:
 Lower Bound = 1, Upper Bound = 18
 Length(CCC) = 18 - 1 + 1 = 18 elements

(b) Address Calculation for Array AAA

The formula to calculate the address of an element in a linear array is:

LOC(AAA[k]) = Base(AAA) + w × (k - Lower Bound)

Where:

Base(AAA) = 300 (address of AAA[5])
w = 4 words per memory cell
k = element index
Lower Bound = 5

For AAA[15]:

 Solution:
 LOC(AAA[15]) = 300 + 4 × (15 - 5)
 = 300 + 4 × 10
 = 300 + 40
 = 340

For AAA[35]:

 Solution:
 LOC(AAA[35]) = 300 + 4 × (35 - 5)
 = 300 + 4 × 30
 = 300 + 120
 = 420

For AAA[55]:

 Solution: 
 AAA[55] is not a valid element of array AAA because 55 exceeds the upper bound of 50.
 The valid index range for AAA is 5 ≤ k ≤ 50.