Section 5

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.

6. 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

7. 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.

8. 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.

9. 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.

10. 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.