Page 12 - TP_Prime_V2.2_Class7
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Step 5: List the last quotient and all the remainders (moving from bottom to top). You will
get your binary number.
Look at the given examples to understand the conversion better.
Example 1: Convert the (26) to binary number.
10
2 2 6 The binary equivalent of (26) is 11010
2 1 3 0
Prime (Ver. 2.2)-VII 2 6 1 In other words, (26) = (11010) 2
10
10
2 3 0
1 1
Start listing the last quotient and all the
remainders from here.
Example 2: Convert the (64) to binary number.
10
10 2 6 4
2 3 2 0
2 1 6 0 The decimal number system is based
2 8 0 (64) = (1000000) 2 on ten digits, likely influenced by
10
2 4 0 the number of human fingers.
2 2 0
1 0
Binary to Decimal Conversion
To convert a binary number into a decimal number, follow these steps:
Step 1: Start from the right-most digit known as the LSD before the fractional point, and
move leftwards.
Step 2: While doing so, multiply each digit by 2 raised to a particular power. The powers
of 2 start from 0 and increase to 1, 2, and so on, as you move leftwards.
Step 3: Add up all the resulting products. You will get your decimal number.
The following examples will help you to understand the conversion.
Example 1: Convert (1111) to decimal. Example 2: Convert (10111) to decimal.
2
2
2
1
4
3
2
3
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 = 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 + 2 0
0
1
= 8 + 4 + 2 + 1 = 16 + 0 + 4 + 2 + 1
= 15 = 23
(1111) = (15) 10 (10111) = (23) 10
2
2

