Question:
The decimal equivalent of the binary number 111111 is:
बाइनरी संख्या 111111 का दशमलव समतुल्य (decimal equivalent) है:
Options:
- 46
- 63
- 52
- 36
- 46
- 63
- 52
- 36
Correct Answer: b)
Explanation:
Converting binary \(111111_2\) to decimal:
\[ 1\cdot 2^5 + 1\cdot 2^4 + 1\cdot 2^3 + 1\cdot 2^2 + 1\cdot 2^1 + 1\cdot 2^0 = 32 + 16 + 8 + 4 + 2 + 1 = 63 \]
Alternatively, for \(n=6\) continuous 1s: \(2^6 – 1 = 64 – 1 = 63\).
बाइनरी \(111111_2\) को दशमलव में बदलने पर:
\[ 1\cdot 2^5 + 1\cdot 2^4 + 1\cdot 2^3 + 1\cdot 2^2 + 1\cdot 2^1 + 1\cdot 2^0 = 32 + 16 + 8 + 4 + 2 + 1 = 63 \]
अथवा \(2^6 – 1 = 64 – 1 = 63\)।