Chapter 3, Problem 7RQ

Program Plan Intro

Decimal number system:

• In binary system, the numbers “0” and “1” are only used.
• It means, in total, binary system has only 2 numbers.
• Therefore, the base used for binary numbering system is 2.

BCD number system:

• Binary Coded Decimal (BCD) refers to a section of binary encodings of decimal numbers.
• Each decimal number will be represented by a fixed number of bits such as four or eight.
• BCD has an advantage of representing each decimal number in four bit pattern. This is also called as “8421” encoding.

Explanation of Solution

b.

Conversion of decimal number 389 to its equivalent BCD:

• Given, decimal number is 389.
• Each digit of the decimal number is converted into four bit binary equivalent.
• A group of four bit binary refers to its corresponding decimal digit.
• Finally, the BCD notation of the given decimal number is noted.
• The following diagram describes the BCD notation of the decimal number 389...

Explanation of Solution

c.

Conversion of decimal number 1678 to its equivalent BCD:

• Given, hexadecimal number is 1678.
• Each digit of the hexadecimal number is converted into four bit binary equivalent.
• A group of four bit binary refers to its corresponding hexadecimal digit.
• Finally, the binary notation of the given hexadecimal number is noted.
• The following diagram describes the binary notation of the hexadecimal number 1678...

Explanation of Solution

d.

Conversion of decimal number 2502 to its equivalent BCD:

• Given, hexadecimal number is 2502.
• Each digit of the hexadecimal number is converted into four bit binary equivalent.
• A group of four bit binary refers to its corresponding hexadecimal digit.
• Finally, the binary notation of the given hexadecimal number is noted.
• The following diagram describes the binary notation of the hexadecimal number 2502...