Lesson Plan Introduction to Number System Binary Number

Lesson Plan Introduction to Number System Binary Number System Bouros Ioannis

Introduction • Number system is the way to represent a number in different forms. • We know the decimal numbering system from the first ranks of elementary school. • It’s time to meet a new world of numbers. Number systems with bases other than 10.

Goal and Learning Objectives • The student can identify a number of different numerical systems. • To help students have a better understanding of what the binary system is, how it is used, and how to use it. • Convert binary numbers to decimal numbers and decimal numbers to binary numbers.

Types of Number system: • Binary Number System: It is the number system with base value 2 means it has only two digits to represent the data. The digits are (0, 1). E. g. 00, 01, 10, 11, 100…. • Decimal Number System: It is the number system with base value 10 means it has 10 -digits to represent the data. The digits are(0 -9). Eg. 0, 1, 2, 3, 4, 5, 6 ……… • Octal Number System: It is the number system with base value 8 means it has 8 digits to represent the data. The digits are ( 0 -7). • Hexadecimal Number System : It is the number system with base value 16 means it has 16 digits to represent the data. The digits are 0, 1, 2, 3……. , 9, A, B, C, D, E, F. Eg. A 2, 2 B

Binary Numbers Computers use the binary number system. In the binary, or base-2, system of numbers, numbers are formed using the digits 0 and 1. Each place in a binary number is associated with a power of 2. Binary numbers are written with the subscript ( )2 so that they are not confused with numbers in the decimal system. A digit in the binary system is called a bit, an acronym for binary digit.

Convert from Decimal to Binary System The position of each digit in the number it’s a power of the system base. E. g. • Decimal system: 1000 10 1 103 102 101 100 2 3 4 1 =2* 103 + 3* 102 + 4* 101 + 1* 100 • Binary system: 8 4 2 1 23 22 21 20 1 1 =1* 23 + 0* 22 + 1* 21 + 1* 20 =8+2+1=(11) 10

Convert from Binary to Decimal System Continuous division of the Number with the base of the system. • Step-1: Divide the Number by 2 (as 2 is the base of the binary number system). • Step-2 : Collect the remainder. • Step-3: Divide the quotient again with 2. • Step-4: Repeat the step 2 & 3 until the quotient is 0. • Step-5: Start from bottom, read the sequence of remainders upwards to the top. E. g. (14)10 =( )2 14 Remainder 7. 3. 1. 1. 0 1 1 1 Binary conversion of the (14)10= (1110)2

Evaluation Example: (1001)2 Worksheet 1 =(1· 2³)+(0· 2²)+(0· 2¹)+(1· 2º) =8+0+0+1 =9 Write each binary number as a decimal number. [Show all steps of your conversion!] • (1011)2 = • (1100)2 = • (10001)2 = • (11011)2 = • (11111)2 =

Evaluation Worksheet 2 Example: (47)10 = Write each decimal number as a binary number. [Show all steps of your conversion!] • (16)10 = • (9)10 = • (50)10 = • (78)10 =