Page 11 - Digital Electronics by harish

Example: To convert the decimal number 0.23 to hexadecimal number.

0.23 x 16 = 3.68 = 0.68 with carry → 3 → 3
0.68 x 16 = 10.88 = 0.88 with carry → 10 → A
0.88 x 16 = 14.08 = 0.08 with carry → 14 → E

Therefore, 0.23 10 = 0.3AE 16

Binary to decimal conversion

i) Integer numbers

The given binary number can be converted to decimal number by using the following
procedure:

Step 1 : Write the binary number
Step 2 : Write the place value (weight) directly under the binary number
Step 3 : If the binary digit is zero, cross out the decimal weight
Step 4 : Add the remaining weights to get the decimal number.

Example: To convert the binary number 1011 to decimal number

Step 1 : 1 0 1 1 (Binary number)
Step 2 : 8 4 2 1 (Place value)
Step 3 : 8 4 2 1 (Cross out)
Step 4 : 11 (Add, to get the decimal number)

Therefore, 1011 2 = 11 10

ii) Fractional numbers

The same procedure used for the integer numbers can be used for fractional numbers also.

Example: To convert the binary number 0.101 to decimal number

Step 1 : 1 0 1 (Binary number)
Step 2 : 0.5 0.25 0.125 (Place value)
Step 3 : 0.5 0.25 0.125 (Cross out)
Step 4 : 0.625 (Add, to get the Decimal number)

Therefore, 0.101 2 = 0.625 10

Binary to octal conversion

The binary numbers for the octal numbers from 0 to7 are given in the following table:

Binary Octal
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

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