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# BINARY NUMBER SYSTEM

BINARY NUMBER SYSTEM

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### BINARY NUMBER SYSTEM

1. 1. Q. What is number system?Answer: It is a system forrepresenting numeric values orquantities using differentsymbols (digits).
2. 2. Q. What is decimal numbersystem?Answer: The decimal numbersystem has base 10. It uses thedigits 0 to 9.
3. 3. Q. What does base or radixmean?Answer: The number of digits(symbols) a number systemuse is called base or radix ofthat number system.
4. 4. Today we will learnBINARY NUMBER SYSTEM
5. 5. Q. What is binary numbersystem?Answer: The binary numbersystem has base 2. It uses thedigits 0 and 1 only.
6. 6. Q. How we write a binarynumber?Answer: The binary number iswritten as (1010)2 because itsbase is 2.
7. 7. COUNTING IN BINARY NUMBERSDecimal Binary Decimal Binary0 0 12 11001 1 13 11012 10 14 11103 11 15 11114 100 16 100005 101 17 100016 110 18 100107 111 19 100118 1000 20 101009 1001 21 1010110 1010 22 1011011 1011 23 10111
8. 8. DIVISION METHOD:i. Divide the number by 2.ii. Put the reminder on rightside.iii. Keep dividing the quotienttill we get the quotient lessthan 2.iv. Record reminders frombottom to top to get theanswer.CONVERSION OF A DECIMAL NUMBER INTOBINARY NUMBERExample: (21)10Answer: (21)10 = (10101)2
9. 9. Activity• Convert (31)10 into its binary equivalent.Answer should be (11111)2
10. 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. 11. EXPANSION METHOD:i. Multiply each digit withits place value.ii. Add these place values.iii. The sum is a decimalnumber.CONVERSION OF A BINARY NUMBER INTODECIMAL NUMBERExample: (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= 29Answer: (11011)2 = (29)10
12. 12. Activity• Convert (11011)2 into its decimalequivalent.Answer should be (27)10
13. 13. Q. What digits are used inbinary number system?Answer: The binary numbersystem uses only 0 and 1.
14. 14. Q. What is the base of binarynumber system?Answer: The base of binarynumber system is 2.
15. 15. Q. Which method is used toconvert a decimal number intobinary numbers?Answer: To convert a decimalnumber into binary numberwe use Division method.
16. 16. Q. Which method is used toconvert a binary numbers intodecimal number?Answer: To convert a binarynumber into decimal numberwe use Expansion method.
17. 17. Home Work• Convert (63)10 into its binaryequivalent.• Convert (100110)2 into its decimalequivalent.
18. 18. • Today we learned binary numbersystem• In next lesson we will learnaddition and subtraction inbinary number system