Excess 3 adder | Logic diagram | STLD | Lec-68

TL;DR

Video explains how to perform addition using Excess-3 code.

Transcript

hi everyone in this video I'm going to explain about access3 order in the previous video I told you about BCD add binary coded decimal ER where if the result is greater than n after addition if the result is greater than 9 there we need to add six to the result okay this is access three add access three add is different whereas in BCD we are perfor... Read More

Key Insights

• ❓ Understanding the binary representation in Excess-3 is foundational for accurate addition calculations.
• ❓ The addition process in Excess-3 differs fundamentally from standard binary addition to incorporate error correction through adjustments of 3 or 13.
• 🇨🇫 Carry handling is a central theme in Excess-3 addition, affecting how results are interpreted and represented.
• 👨‍💻 Practical examples serve as an effective tool for grasping the nuances of Excess-3 code arithmetic.
• 🫦 A logic diagram is provided to support the implementation of the Excess-3 addition process using a 4-bit parallel adder IC.
• ❓ Excess-3 encoding emphasizes mathematical transformations to facilitate easier calculations while encoding decimal values.
• 🎭 The video offers crucial methods for converting results back to decimal from their binary forms after performing arithmetic operations.

Questions & Answers

Q: What is Excess-3 code and how does it differ from BCD?

Excess-3 code is a non-weighted code used to express decimal numbers. Unlike Binary Coded Decimal (BCD), where decimal digits are directly represented by their binary equivalent, Excess-3 adds 3 to each decimal digit before converting it to binary, offsetting the representation. Thus, for example, the decimal value of 0 is represented as 0011 (3 added), contrasting with the binary representation of 0000 in BCD.

Q: How do you determine the adjustment needed during Excess-3 addition?

When adding two Excess-3 numbers, if a carry is generated during the addition of the binary equivalents, you add 3 to the result. Conversely, if no carry is generated, you can add 13 to the result. This ensures the correct representation of the decimal equivalent in Excess-3 format, aligning the binary result with its intended decimal output.

Q: Can you provide an example to clarify Excess-3 addition?

Certainly! For adding 9 and 5 in Excess-3, first convert these numbers to their Excess-3 representations (12 and 8, respectively). After performing binary addition, if you generate a carry, add 3 to your result. For this case, the initial binary outcome indicates carry, leading to adjustment and ultimately yielding the Excess-3 output that reflects the sum, which is 14.

Q: What are the rules for handle carry in Excess-3 addition?

In Excess-3 addition, if the initial binary addition results in a carry of one, add 3 to your result. If there's no carry, you should add 13 to ensure the outcome remains valid. This method of adjustment is critical to maintaining the integrity of the Excess-3 coded result.

Summary & Key Takeaways

• The video outlines the process of Excess-3 addition, focusing on how to add two Excess-3 encoded numbers by first understanding their binary representations.

• It emphasizes the need to handle carries during addition differently by introducing rules for when a carry is generated or not, leading to adjustments in the results.

• Finally, the video offers practical examples demonstrating how to apply these rules, encapsulated with a logic diagram for a 4-bit parallel adder that operates in Excess-3.