Binary to Decimal Number Conversion

Converting Binary to Decimal Numbers

• Binary numbers are base 2.
• Decimal numbers are base 10.
• Binary digits consist of 0 or 1.

Conversion Process

• The conversion process starts from the rightmost digit of the binary number.
• The rightmost digit is associated with 2^0.
• Move from right to left, associating each subsequent digit with an increasing power of 2 (2^1, 2^2, 2^3, etc.).
• Each binary digit is multiplied by its corresponding power of 2.
• Add the results, and this gets the decimal equivalent.

Example 1

• To convert the binary number 1010 to decimal:
• 0 * 2^0 = 0
• 1 * 2^1 = 2
• 0 * 2^2 = 0
• 1 * 2^3 = 8
• The decimal equivalent is: 8 + 0 + 2 + 0 = 10

Useful Powers of 2

• Using these values speeds up conversion
• 2^0 = 1
• 2^1 = 2
• 2^2 = 4
• 2^3 = 8
• 2^4 = 16
• 2^5 = 32
• 2^6 = 64
• 2^7 = 128
• 2^8 = 256

Example 2

• To convert the binary number 11011:
• 1 * 2^0 = 1
• 1 * 2^1 = 2
• 0 * 2^2 = 0
• 1 * 2^3 = 8
• 1 * 2^4 = 16
• The decimal equivalent is: 16 + 8 + 0 + 2 + 1 = 27

Converting Fractional Binary Numbers

• Numbers to the left of the decimal point use positive powers of 2 (2^0, 2^1, 2^2, etc.).
• Numbers to the right of the decimal point use negative powers of 2 (2^-1, 2^-2, 2^-3, etc.).
• 2^-1 = 1/2
• 2^-2 = 1/4
• 2^-3 = 1/8

Example of Fractional Conversion

• To convert the binary number 1100.101:
• 0 * 2^-3 = 0
• 0 * 2^-2 = 0.25
• 1 * 2^-1 = 0.5
• 0 * 2^0 = 0
• 0 * 2^1 = 0
• 1 * 2^2 = 4
• 1 * 2^3 = 8

Conversion of Negative Powers

• 2^-n is the same as 1 / 2^n
• For Example: 2^-4 = 1/16

Learn how to convert binary numbers to decimal numbers. This conversion involves multiplying each binary digit by powers of 2 and summing the results. Includes examples and a table of useful powers of 2.