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The given examples will help you understand the conversion.
Example 1: Convert (125) to a decimal Example 2: Convert (5AD) to a decimal number.
16
16
number. A = 10 (since A represents 10 in hexadecimal)
1
= 1 × 16 +2 × 16 + 5 × 16 0 D = 13 (since D represents 13 in hexadecimal)
2
2
1
= 1 × 256 + 2 × 16 + 5 × 1 = 5 × 16 + 10 × 16 + 13 × 16 0
= 256 + 32 + 5 = 5 × 256 + 10 × 16 + 13 × 1
= 293 = 1280 + 160 + 13
= 1453
Therefore, (125) = (293) 10 Therefore, (5AD) = (1453)
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DECIMAL TO BINARY NUMBER SYSTEM 16 10

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

Step 1 Divide the given decimal number by 2 and note the remainder.
Step 2 Divide the quotient obtained from the previous step by 2 and note the new remainder.

Step 3 Repeat the steps until the quotient becomes less than 2.

Step 4 Write the remainders in reverse order, starting with the last remainder.

Example 1: Convert (13) to a binary number. Example 2: Convert (28) to a binary number.
10
10
2 13 2 28
2 6 1 2 14 0

2 3 0 2 7 0
1 1 2 3 1
1 1
Therefore, (13) = (1101) 2
10
Therefore, (28) = (11100) 2
10
DECIMAL TO OCTAL NUMBER SYSTEM

To convert a decimal number to octal, follow these steps:
Step 1 Divide the given decimal number by 8 and note the remainder.

Step 2 Divide the quotient obtained from the previous step by 8 and note the new remainder.

Step 3 Repeat the steps until the quotient becomes less than 8.

Step 4 Write the remainders in reverse order, starting with the last remainder.

Example 1: Convert (1023) to an octal number. Example 2: Convert (4320) to an octal number.
10
10
8 1023 8 4320
8 127 1 8 540 0
8 15 0 8 67 4

1 1 8 8 3
1 0

Therefore, (1023) = (1777) 8
10
Therefore, (4320) = (10340) 8
10

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Number System