Background: The Excess$-3($XS$-3)$ binary code is often used in digital systems,

especially in computing systems where decimal digit manipulations are necessary,

such as in calculators and digital clocks. The Excess$-3$ code for a decimal digit is

formed by adding three to the decimal digit and then converting that sum to its

binary equivalent.

Specification: Design a digital circuit that converts a Binary$-$Coded Decimal $($BCD$)$

input to its corresponding Excess$-3$ code output.

Requirements:

Understanding Excess$-3$ Encoding: Research and explain how the Excess$-$

$3$ encoding scheme works and why it might be used instead of the regular

BCD representation.

Circuit Design: Using logic gates, design a circuit that takes a $4-$bit BCD

input and outputs a $4-$bit Excess$-3$ code. The BCD inputs will be in the range

of $0000(0$ in decimal$)$ to $1001(9$ in decimal$).$

Truth Table: Construct a truth table that maps each BCD input to its

corresponding Excess$-3$ output.

Optimization: Optimize your circuit to use the minimum number of gates.

Use Karnaugh Maps with considering don't care $(x)$ and present a simplified

Boolean expression for each output bit.

Implementation: Create a schematic diagram of your optimized circuit

using any digital design software.

Deliverables:

A report that includes your research on Excess$-3$ encoding, truth table, K$-$

map, optimized Boolean expressions, and schematic diagram of the circuit.