Convert the binary number (101010)₂ to its decimal equivalent.

Explanation

To convert the binary number (101010)₂ into decimal, we apply the binary-to-decimal conversion method by multiplying each bit by 2 raised to the power of its positional index (starting from 0 on the right). (101010)2 =1×25+0×24+1×23+0×22+1×21+0×20 (101010)2 =32+0+8+0+2+0 (101010)2 =42 Thus, the decimal equivalent of (101010)₂ is 42. Important Key Points: 1. Binary-to-decimal conversion involves multiplying each bit by powers of 2, starting from the rightmost bit. 2. This conversion method is essential in computing, especially in low-level data operations. Knowledge Booster: • Binary System: It is a base-2 numeral system consisting of only 0s and 1s, which is fundamental in computer operations. • Decimal System: It is a base-10 numeral system, the standard system used for representing integer values in daily life. • Octal System: Another numeral system with a base of 8, often used in computing, especially in legacy systems. • Hexadecimal System: A base-16 numeral system widely used in programming and computing to represent large binary numbers in a more compact form. 42 www.bankersadda.com | Adda247 App