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Example 2: To convert (100101) into decimal number.
2
(100101) = 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 0 × 2 + 1 × 2 0
3
2
5
4
1
2
= 1 × 32 + 0 × 16 + 0 × 8 + 1 × 4 + 0 × 2 + 1 × 1
= 32 + 0 + 0 + 4 + 0 + 1
= 37
Thus, (100101) = (37)
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Knowledge Discovery Subject Enrichment

If the last digit of a binary number is 1, the number is odd; if it’s 0, the number is even. For example, the
number 101 in binary system is an odd number equal to number 5 in decimal system, while the number
1010 in binary system is an even number equal to number 10 in decimal system.

Try This
Computational Skills
Convert the numbers given below as directed:
(a) 10111 into decimal number system _______________
(b) 137 into binary number system _______________
(c) 100010 into decimal number system _______________
(d) 78 into binary number system _______________

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.

BINARY ADDITION
The basic rules for binary addition are listed in the table below:

Case Input Sum Carry

1 0 + 0 0 0

2 0 + 1 1 0

3 1 + 0 1 0
4 1 + 1 0 *1

*Carry of 1 is shifted to the next column to the left of the current digit.

Example 1 Example 2 Example 3

Compute (101) + (100) Compute (1011) + (1101) Compute (11111) + (1001)
2 2 2 2 2 2
1 1 1 Carry 1 1 1 1 Carry
1 0 1 1 0 1 1 1 1 1 1 1
+ 1 0 0 + 1 1 0 1 + 1 0 0 1
1 0 0 1 1 1 0 0 0 1 0 1 0 0 0

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