Here's the reference material which has me confused.
A derivation of a 6-64 tree decoder using only 2-4 decoders and 2-input and gates
Sample reference material on line tree decoder vs line matrix decoder
After reviewing these 2 images I am confused about the differences between the 2 as the 6 to 64 decoder looks remarkably like a matrix decoder albeit with additional and gates.
Are there any conventional size (eg 2-4 decoders only) or structure restrictions?
Or is a matrix decoder just 2 line tree decoders laid at 90 degree angles of one another?
2 Answers 2
Good question. That 2^(m+1)-4 expression is for line tree decoders, also mentioned in question 1(b). Please see the figure on the left-hand side of page 16 on the Memory section. For a line tree decoder, you always start with a 2-4 decoder, and at each stage we add one input at a time requiring twice as many 2-input AND gates as the previous level.
In question 1(a), we are basically using a matrix decoder (see the right-hand side figure on page 16), and the number of AND gates for a matrix decoder does not follow the formula for a line tree decoder - same goes with the matrix decoder on page 16. For the matrix decoder in question 1(a), it consists of two 3-to-8 line tree decoders (where we remember a 3-to-8 line decoder can be made up of 8 gates and a 2-to-4 decoder) in X and Y dimensions and the 2-dimensional AND-gate array.
Questions referenced are for those in your problem set. Example figures are referenced from your course's slideshow notes.
Line tree decoders follow a hierarchical tree structure with a sequential decoding process, whereas matrix decoders use a matrix structure for more flexible input to output mappings. Line tree decoders have lower decoding delays and are suitable for applications where decoding speed is critical.
Matrix decoders provide more flexibility in mapping input codes to outputs, but may have higher decoding delays making them suitable for application with complex decoding patterns.