Section 5 Digital Electronic Circuits

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.

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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: Binary weight:8421

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 2 n - 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.