Question

You are given four 12-bit numbers A,B,C,D in 16-bit registers. You have a 4-bit comparator and a 4-bit adder. Using as few and as small multiplexers and counters as possible, and with minimum additional registers, design a bit-serial system that finds two largest numbers and their sum. In addition to proper design, write down the sequence of operations that need to be done in each clock cycle and design required FSM using counter and combinatorial gates.

Answer 1

To design a bit-serial system that finds the two largest numbers and their sum, use multiplexers, counters, and combinatorial gates. Follow a sequence of operations involving loading numbers, performing comparisons, selecting and storing the largest numbers, calculating the sum, and storing the result.

Step-by-step explanation:

To design a bit-serial system that finds the two largest numbers and their sum, we can use a combination of multiplexers, counters, and combinatorial gates. Here are the steps:

1. Initialize a 4-bit counter to count from 0 to 3.
2. Load the four 12-bit numbers A, B, C, and D into 16-bit registers.
3. Compare the numbers using the 4-bit comparator and determine the largest number.
4. Use multiplexers to select the largest number and store it in a register.
5. Repeat steps 3 and 4 to find the second largest number.
6. Use the 4-bit adder to calculate the sum of the two largest numbers.
7. Store the sum in a register.

The sequence of operations in each clock cycle would involve loading the numbers into registers, performing comparisons using the comparator, selecting and storing the largest numbers, and finally calculating and storing the sum using the adder.

An FSM (Finite State Machine) can be used to control the sequence of these operations, based on the clock cycle and the state of the counter.