The document discusses number systems and binary numbers. It defines a number system as a way of naming or representing numbers, and binary number system as a system that uses only two digits, 0 and 1. It explains how to write binary numbers with a base of 2. It then shows a table converting decimal numbers to their binary equivalents from 0 to 15. Finally, it outlines two methods for converting between decimal and binary numbers: division and expansion.

1. SUBMITTED TO: Mr. Bhanu
BHUSHAN Parashar
(Assistant Professor-II)
Submitted by: Ankit Gupta
(Bca 1st year)

3. Any system of naming or representing numbers, as the decimal
system or the binary system.
WHAT IS NUMBER SYSTEM ?

4. The binary number system is a numbering system that represents
numeric values using two unique digits (0 and 1).
WHAT IS BINARY NUMBER SYSTEM ?

5. The binary number written as (1010101)2 because its base is 2 .
HOW TO WRITE BINARY NUMBER ?

6. DECIMAL BINARY
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
COUNTING IN BINARY NUMBER

7. DIVISION METHOD:
1. Divide the number.
2. Put the remainder on
right side.
3. Keep dividing the quotient
till we get the quotient less
than 2.
4. Record reminders from bottom
to top to get the answer .
CONVERSION OF DECIMAL NUMBER
INTO BINARY NUMBER
2
2
2
2
NUMBER
21
10
5
2
1
REMINDER
1
0
1
0
Answer : (21)2 =(10101)2

8. EXPANSION METHOD: EXAMPLE:(11101)2
1. Multiply each digit with =(1*24)+(1*23)+(1*22)+(0*21)+(1*20)
Its place value. =(1*16)+(1*8)+(1+4)+(0*2)+(1*1)
2. Add these place value. =16+8+4+0+1
3. The sum is decimal number. =29
Answer:(11101)2=2910
CONVERSION OF BINARY NUMBER INTO
DECIMAL NUMBER

9. THANK
YOU