Digital Circuit Design with an Introduction to CPLDs and FPGAs

# Chapter 4: Binary Codes

## Overview

This chapter describes the most commonly used binary codes. In particular, we will discuss the Binary Coded Decimal (BCD), the Excess-3 Code, the 2*421 Code, the Gray Code, and the American Standard Code for Information Interchange (ASCII) code. We will also discuss parity bits.

## 4.1 Encoding

In general, encoding is the process of putting a message into a code. In this text, encoding will refer to a process where the decimal numbering system as well as other alphanumerics (combinations of numbers and letters) are represented by the digits of the binary numbering system, that is 0 and 1. In this section we will introduce four different codes where 4 bits are used to represent a single decimal character.

### 4.1.1 Binary Coded Decimal (BCD)

The Binary Coded Decimal (BCD) uses 4 bits to represent the decimal numbers 0 through 9 and these are shown in the Table 4.1. This code is also known as 8421 code because the digits 8, 4, 2 , and 1 represent the weight of its bits position. In other words, the BCD is a weighted code.

Table 4.1: The BCD code

Decimal

BCD

0

0000

1

0001

2

0010

3

0011

4

0100

5

0101

6

0110

7

0111

8

1000

9

1001

We observe that only ten of the sixteen (2 4) possible combinations are used in BCD; the remaining six combinations 1010, 1011, 1100, 1101, 1110, and 1111 are invalid in BCD. The designations A through F to represent...