BINARY NUMBER SYSTEM
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The document discusses the binary number system. It begins by defining number systems and the decimal system. It then introduces the binary number system which has a base of 2 and uses only the digits 0 and 1. It shows how to write binary numbers and provides a table to demonstrate counting and place values in the binary system. The document explains two methods for converting between decimal and binary numbers - the division method to convert decimals to binary, and the expansion method to convert binary to decimal. It includes examples and practice problems for students to convert numbers between the two number systems.
BINARY NUMBER SYSTEM
- 1. Q. What is number system? Answer: It is a system for representing numeric values or quantities using different symbols (digits).
- 2. Q. What is decimal number system? Answer: The decimal number system has base 10. It uses the digits 0 to 9.
- 3. Q. What does base or radix mean? Answer: The number of digits (symbols) a number system use is called base or radix of that number system.
- 4. Today we will learn BINARY NUMBER SYSTEM
- 5. Q. What is binary number system? Answer: The binary number system has base 2. It uses the digits 0 and 1 only.
- 6. Q. How we write a binary number? Answer: The binary number is written as (1010)2 because its base is 2.
- 7. COUNTING IN BINARY NUMBERS Decimal Binary Decimal Binary 0 0 12 1100 1 1 13 1101 2 10 14 1110 3 11 15 1111 4 100 16 10000 5 101 17 10001 6 110 18 10010 7 111 19 10011 8 1000 20 10100 9 1001 21 10101 10 1010 22 10110 11 1011 23 10111
- 8. DIVISION METHOD: i. Divide the number by 2. ii. Put the reminder on right side. iii. Keep dividing the quotient till we get the quotient less than 2. iv. Record reminders from bottom to top to get the answer. CONVERSION OF A DECIMAL NUMBER INTO BINARY NUMBER Example: (21)10 Answer: (21)10 = (10101)2
- 9. Activity • Convert (31)10 into its binary equivalent. Answer should be (11111)2
- 10. Q. What is the place value 2 in (1259)10? Answer: The place value of 2 in (1259)10 is 2×100 = 2×102 = 200.
- 11. EXPANSION METHOD: i. Multiply each digit with its place value. ii. Add these place values. iii. The sum is a decimal number. CONVERSION OF A BINARY NUMBER INTO DECIMAL NUMBER Example: (11101)2 =(1×24 )+ (1×23 )+(1×22 )+(0×21 )+(1×20 ) =(1×16)+ (1×8) +(1×4)+ (0×2)+(1×1) = 16 + 8 + 4 + 0 + 1 = 29 Answer: (11011)2 = (29)10
- 12. Activity • Convert (11011)2 into its decimal equivalent. Answer should be (27)10
- 13. Q. What digits are used in binary number system? Answer: The binary number system uses only 0 and 1.
- 14. Q. What is the base of binary number system? Answer: The base of binary number system is 2.
- 15. Q. Which method is used to convert a decimal number into binary numbers? Answer: To convert a decimal number into binary number we use Division method.
- 16. Q. Which method is used to convert a binary numbers into decimal number? Answer: To convert a binary number into decimal number we use Expansion method.
- 17. Home Work • Convert (63)10 into its binary equivalent. • Convert (100110)2 into its decimal equivalent.
- 18. • Today we learned binary number system • In next lesson we will learn addition and subtraction in binary number system