The document outlines the conversion methods for binary numbers to decimal, octal, and hexadecimal, providing examples for each type of conversion. It explains the steps for converting both whole and fractional binary numbers into these numbering systems, detailing the importance of grouping the binary digits appropriately. Additionally, it includes various examples to illustrate the conversion processes clearly.

1. Government College of Pharmacy, Ratnagiri
Computer Applications
in Pharmacy
Sub In charge : Shital B. Thakur
(BE Computer)

2. Number Systems

3. Learning Objectives
In this chapter you will learn about
• Conversion of Binary to Decimal
• Conversion of Binary to Octal
• Conversion of Binary to Hexadecimal
(Continued on next slide)

4. Converting a Binary Number to its Equivalent
Decimal number
Given binary number is 10100011.
Ex. (10100011)2 =
(1 × 27) + (0 × 26) + (1 × 25) + (0 × 24) + (0 × 23) + (0 × 22) + (1 × 21) + (1 × 20)
= 128 + 0 + 32 + 0 + 0 + 0 + 2 + 1.
= 163.
Ex. 10101 Binary To Decimal Conversion:
The given Binary Number = 101012
step 1: Write summation of multiplication of each bit with increasing
power of 2 from the right to left of the binary number 10101.
1 x 24 + 0 x 23 + 1 x 22 + 0 x 21 + 1 x 20
step 2: Simplify the above expression
16 + 0 + 4 + 0 + 1 = 21
101012 = 2110

5. Converting a Binary fraction Number to its
Equivalent Decimal number
Ex. 101.1101 =
Ex. (10110.111)2=()10
(1*2)4+(0*2)3+(1*2)2+(1*2)1+(0*2)0
=16+0+4+2+0
=22
For Fractional Part
.111
=1*2-1+1*2-2+1*2-3
1*1 + 1*1 + 1*1
21 22 23
0.5+0.25+0.125=0.875
Final answer: (10110.111)2=(22.875)10

6. Converting a Binary Number to its Equivalent
Octal Number
Method
Step 1: Divide the digits into groups of three
starting from the right
Step 2: Convert each group of three binary digits to
one octal digit using the method of binary to
decimal conversion
(Continued on next slide)

7. (Continued from previous slide..)
Shortcut Method for Converting a Binary Number
to its Equivalent Octal Number
Example
11010102 = ?8
Step 1: Divide the binary digits into groups of 3 starting
from right
001 101 010
Step 2: Convert each group into one octal digit
0012 = 0 x 22 + 0 x 21 + 1 x 20 = 1
1012 = 1 x 22 + 0 x 21 + 1 x 20 = 5
0102 = 0 x 22 + 1 x 21 + 0 x 20 = 2
Hence, 11010102 = 1528
R

8. Shortcut Method for Converting a Binary
Number to its Equivalent Octal Number

9. Conversion Binary fraction to Octal
Ex. 010111101.101110110
010 111 101 . 101 110 110
=275.566

10. Shortcut Method for Converting a Binary
Number to its Equivalent Hexadecimal Number
Method
Step 1:
Step 2:
Divide the binary digits into groups of four
starting from the right
Combine each group of four binary digits to
one hexadecimal digit
(Continued on next slide)

11. Shortcut Method for Converting a Binary
Number to its Equivalent Hexadecimal Number
(Continued from previous slide..)
Example
1111012 = ?16
Step 1: Divide the binary digits into groups of four
starting from the right
0011 1101
Step 2: Convert each group into a hexadecimal digit
00112
11012
= 0 x 23 + 0 x 22 + 1 x 21 + 1 x 20 = 310
= 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 1310
= 316
= D16
Hence, 1111012 = 3D16

12. Conversion Binary fraction to Hexadecimal
Ex. 11101110.011011
1110 1110 . 0110 1100
14 14 .6 12
=EE.6C
EX. 0110 1110 0110 1110 1011

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