--- title: "Largest of four integers processor" subject: "Embedded System" chapter: 2 key: "semester_6/embedded_system:spp-largest-of-four" source: https://www.bctengineer.com/q/semester_6/embedded_system/spp-largest-of-four site: BCT Engineering --- # Largest of four integers processor Embedded System · Chapter 2: Hardware Design Issues - Asked in: 2073 Bhadra, 8 marks - Video: [Designing Single Purpose Processor To Calculate GCD (HCF).](https://www.youtube.com/watch?v=Wy344fMRnOo) — AFlick - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/embedded_system/spp-largest-of-four - Whole chapter: https://www.bctengineer.com/md/semester_6/embedded_system/chapter-2 ## Question Develop algorithm; draw the state diagram and design the datapath of a custom single purpose processor that determines the largest of four integers. Propose the block diagram of its controller also. ## Short answer The algorithm initializes max = a, then sequentially compares b, c, d, updating max if larger. The datapath uses a 4:1 mux, comparator, and max register; the controller is a 6-state FSM with inputs start and gt, outputs sel, load, out_en. ## Answer **Assumption:** four 8-bit integers a, b, c, d are available on input ports; the processor outputs the largest value when *start* is given. #### Algorithm ```text max = a if (b > max) max = b if (c > max) max = c if (d > max) max = d output max ``` #### State diagram (FSMD) ```text S0 --start--> S1 (MAX=a) --> S2 (if b>MAX: MAX=b) ^ | | v S5 (out=MAX, done) <-- S4 (if d>MAX: MAX=d) <-- S3 (if c>MAX: MAX=c) ``` | State | Actions | Condition / next | |---|---|---| | S0 wait | done = 0 | start = 0: stay in S0; start = 1: S1 | | S1 | MAX = a | S2 | | S2 | if gt then MAX = b | S3 | | S3 | if gt then MAX = c | S4 | | S4 | if gt then MAX = d | S5 | | S5 | out = MAX, done = 1 | S0 | (gt = comparator output "selected input > MAX".) #### Datapath ```text a --+ b --+--> [4:1 mux] --+--> [ > comparator ] --> gt c --+ (sel 2b) | ^ d --+ | | v | [ MAX register ]-+ | v out ``` Components: a 4:1 multiplexer selecting the input (sel = 00 a, 01 b, 10 c, 11 d), an 8-bit comparator (selected input > MAX), an 8-bit register MAX with load enable (load = gt, or unconditional in S1), and an output buffer. Control signals: sel[1:0], load, out_en. #### Controller block diagram ```text start, status flags --> +-------------+ +-----------+ (from datapath) | Next-state |-->| State | | logic | | register | +------^------+ +-----+-----+ | current state | +-----------------+ v +-------------+ | Output logic|--> control +-------------+ signals ``` 6 states, 3-bit state register. Output logic: S1: sel = 00, ld = 1; S2: sel = 01, ld = gt; S3: sel = 10, ld = gt; S4: sel = 11, ld = gt; S5: out_en = 1, done = 1. The controller's inputs are *start* and the status signal *gt* from the datapath. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the basic algorithm for largest of four? A. Sort all four numbers fully B. Set max = a, then compare b, c, d in turn and update max if larger C. Add the four numbers and divide by 4 D. Compare a with d only Answer: B. A running maximum is updated whenever the next input exceeds it. (Key point: Algorithm) 2. When is MAX loaded in states S2-S4? A. Always B. Only when start = 1 C. Only when gt (selected input > MAX) is true D. Only when done = 1 Answer: C. The comparator output gt controls the load enable of the MAX register. (Key point: Load condition) 3. What is the 4:1 multiplexer for? A. Selecting the output buffer B. Selecting the state C. Counting the inputs D. Selecting which of a, b, c, d goes to the comparator and register Answer: D. A 2-bit select (00 a, 01 b, 10 c, 11 d) feeds one input at a time to the comparator. (Key point: Datapath multiplexer) 4. How many states does the controller have, and how wide is the state register? A. 6 states, 3 bits B. 4 states, 2 bits C. 5 states, 3 bits D. 6 states, 6 bits Answer: A. S0-S5 are six states, so a 3-bit binary state register is needed. 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