Page 26 - CodePilot V5.0 C7

Step 2 The powers of 2 should start at 0 and increase by 1 as you move left.

Step 3 Simplify each product and add them together to get the decimal equivalent.

The given examples will help you understand the conversion.
Example 1: Convert (11010) to a decimal number.
2
2
1
3
4
= 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + 0 × 2 0
= 16 + 8 + 0 + 2 + 0
= 26
Therefore, (11010) = (26) 10
2
Example 2: Convert (10111101) to a decimal number.
2
6
2
7
1
3
4
5
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 0
= 128 + 0 + 32 + 16 + 8 + 4 + 0 + 1
= 189
Therefore, (10111101) = (189) 10
2
OCTAL TO DECIMAL NUMBER SYSTEM
To convert an octal number to a decimal number, follow these steps:
Step 1 Multiply each digit of the given octal number by the corresponding power of 8, starting

from the rightmost digit.
Step 2 The powers of 8 should start at 0 and increase by 1 as you move from right to left.

Step 3 Simplify each product and add them together to get the decimal equivalent.

The given examples will help you understand the conversion.
Example 1: Convert (175) to a decimal number. Example 2: Convert (314) to a decimal number.
8
8
= 1 × 8 + 7 × 8 + 5 × 8 0 = 3 × 8 + 1 × 8 + 4 × 8 0
1
2
2
1
= 1 × 64 + 7 × 8 + 5 × 1 = 3 × 64 + 1 × 8 + 4 × 1
= 64 + 56 + 5 = 192 + 8 + 4
= 125 = 204
Therefore, (175) = (125) 10 Therefore, (314) = (204) 10
8
8
HEXADECIMAL TO DECIMAL NUMBER SYSTEM

To convert a hexadecimal number to a decimal number, follow these steps:

Step 1 Multiply each digit (or alphabet value) of the given hexadecimal number by the
corresponding power of 16, starting from the rightmost digit.

Step 2 The exponents of 16 should start with 0 for the rightmost digit and increase by 1 as you
move left.
Step 3 Simplify each product and add them together to get the decimal equivalent.

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CodePilot (V5.0)-VII