Question

81.a which of these numbers, which are written in binary, are even? why? convert them into base 10. 101001 answer clear all the number even. the number converted into decimal is. grade answer learning tools textbook and examples

Explanation:

Step1: Check if binary number is even

A binary number is even if its last digit (least significant bit) is 0, because the last digit represents \(2^0 = 1\), and if it's 0, the number is divisible by 2. The binary number \(101001\) has last digit \(1\), so it's not even.

Step2: Convert binary to decimal

To convert binary \(101001\) to decimal, use the formula \( \sum_{i = 0}^{n - 1} b_i \times 2^i \), where \(b_i\) is the \(i\)-th bit from the right (starting at 0).
For \(101001\) (bits from right: \(1, 0, 0, 0, 1, 0\) wait, no, from left: positions 5 to 0 (since 6 bits: \(2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)):
\(1\times2^5 + 0\times2^4 + 1\times2^3 + 0\times2^2 + 0\times2^1 + 1\times2^0\)
\(= 32 + 0 + 8 + 0 + 0 + 1\)
\(= 41\)

Answer:

The number \(101001\) is not even (because its least significant bit is 1). The number converted into decimal is \(41\).