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Example 1 Example 2

To convert the decimal number To convert the decimal number 145 into
35 into its binary equivalent. its binary equivalent.

2 35 2 145
2 17 Remainder 1
2 72 Remainder 1
2 8 Remainder 1 2 36 Remainder 0
2 4 Remainder 0 2 18 Remainder 0

2 2 Remainder 0 2 9 Remainder 0

2 1 Remainder 0 2 4 Remainder 1
0 Remainder 1 2 2 Remainder 0

2 1 Remainder 0

0 Remainder 1

1 0 0 0 1 1 Thus, the decimal number 145
Thus, the decimal number 35
is equal to 100011 in binary form. is equal to 10010001 in binary form.
It is expressed as (35) = (100011) It is expressed as (145) = (10010001) 2 1 0 0 1 0 0 0 1
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Conversion of Binary Number into Decimal Number

To convert a binary number into a decimal number:
• Write the place value of every digit of the binary number by multiplying it with the correct
power of the base 2, starting with power 0 from the extreme right.
• Add the result of each multiplication to get the decimal number.

Example 1: To convert (11001) into decimal number.
2
(11001) = 1 × 2 + 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 0
4
3
1
2
2
= 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1
= 16 + 8 + 0 + 0 + 1
= 25
Thus, (11001) = (25) 10
2
Example 2: To convert (100101) into decimal number.
2
(100101) = 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 0 × 2 + 1 × 2 0
3
4
2
1
5
2
= 1 × 32 + 0 × 16 + 0 × 8 + 1 × 4 + 0 × 2 + 1 × 1
= 32 + 0 + 0 + 4 + 0 + 1
= 37
Thus, (100101) = (37) 10
2
Binary Arithmetic
The arithmetic of binary numbers involves the addition, subtraction, multiplication, and division
of binary numbers. Binary arithmetic operations usually start from the rightmost digit.

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