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Understanding the Binary Number System and BCD Code

This chapter introduces the binary number system, a base-two system using only the digits 0 and 1. Students will learn how to identify the place value of each bit in a binary number, convert binary numbers to decimal, and vice versa. Additionally, the chapter covers the 8421 BCD code, a method for representing decimal digits (0-9) using four binary digits. Key concepts include the significance of place values, conversion techniques, and the application of binary numbers in digital and computer systems. Mastering these skills is fundamental for digital electronics.

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Understanding the Binary Number System and BCD Code

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  1. Section 5 Digital Electronic Circuits

  2. Chapter 32 Binary Number System

  3. Objectives • After completing this chapter, the student should be able to: • Describe the binary number system. • Identify the place value for each bit in a binary number. • Convert binary numbers to decimal numbers. • Convert decimal numbers to binary numbers. • Convert decimal numbers to 8421 BCD code. • Convert 8421 BCD code numbers to decimal numbers.

  4. Binary numbers • The binary system is a base-two system. • It contains two digits, 0 and 1. • The position of the 0 or 1 in the number indicates its value within the number. • The place value of the digits in a binary number increases by the powers of two.

  5. BCD code • An 8421 code is a binary-coded-decimal (BCD) code. • Consists of four binary digits. • Used to represent the digits 0 through 9. • The 8421 designation refers to the binary weight of the 4 bits: Powers of 2: 23 22 21 20 Binary weight: 8 4 2 1

  6. In Summary • The binary number system: • Is the simplest number system. • Contains two digits, 0 and 1. • Used to represent data for digital and computer systems. • Binary data are represented by binary digits called bits. • Bit is derived from binary digit.

  7. The place value of each higher digit’s position in a binary number is increased by a power of 2. • The largest value that can be represented by a given number of places in base 2 is 2n - 1, where n represents the number of bits. • The value of a binary digit can be determined by adding the product of each digit and its place value.

  8. Fractional numbers are represented by negative powers of 2. • To convert from a decimal number to a binary number, divide the decimal number by 2, writing down the remainder after each division. The remainders, taken in reverse order, form the binary number.

  9. The 8421 code, a binary-coded-decimal (BCD) code, is used to represent digits 0 through 9. • The advantage of the BCD code is ease of converting between decimal and binary forms of a number.

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