Question

In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1 . That is, F0=0,F1=1, and Fn=Fn−1+Fn−2,∀n>1 We would like to design a BCD (Binary-Coded-Decimal) Fibonacci number detector g(A,B,C,D) using four inputs A,B,C,D (note that A is the most significant bit and D is the least significant bit in 4-bit ABCD ).

(a) (4\%) Draw a Karnaugh Map of g(A,B,C,D).

Answer 1

To create a BCD Fibonacci number detector g(A,B,C,D), identify the BCD representations of Fibonacci numbers, place them on a Karnaugh Map with the 1s and 0s, and then simplify the map to find the minimum expression that detects these numbers.

Step-by-step explanation:

To design a BCD Fibonacci number detector g(A,B,C,D) using four inputs A, B, C, D, you'll need to create a Karnaugh Map with these inputs representing the digits in a 4-bit Binary-Coded Decimal. First, identify which 4-bit binary numbers correspond to Fibonacci numbers. In the Fibonacci sequence, the first several numbers are 0, 1, 1, 2, 3, 5, 8, etc. In BCD (which only represents decimal numbers 0-9), the relevant Fibonacci numbers are 0, 1, 2, 3, 5, and 8, corresponding to the binary representations 0000, 0001, 0010, 0011, 0101, and 1000.

Place these binary codes into the Karnaugh Map, assigning 1 to the cells that represent the Fibonacci numbers and 0 to all other cells. The Karnaugh Map for g(A,B,C,D) will have 16 cells representing all possible combinations of the 4-bit inputs. The objective now is to simplify the combination of cells to find the minimum expression for g(A,B,C,D), which detects BCD representations of Fibonacci numbers.