A) \[{{(111111)}_{2}}\]
B) \[{{(101111)}_{2}}\]
C) \[{{(111001)}_{2}}\]
D) \[{{(111101)}_{2}}\]
Correct Answer: D
Solution :
Key Idea: Binary numeral system is also known as base 2 numerals. The given number is first converted from binary to decimal equivalence \[{{(100010)}_{2}}={{2}^{5}}\times 1+{{2}^{4}}\times 0+{{2}^{3}}\times 0\] \[+{{2}^{2}}\times 0+{{2}^{1}}\times 1+{{2}^{o}}\times 0\] \[=32+0+0+2+0\] \[={{(34)}_{10}}\] and \[{{(11011)}_{2}}={{2}^{4}}\times 1+{{2}^{3}}\times 1\] \[+{{2}^{2}}\times 0+{{2}^{1}}\times 1\times {{2}^{o}}\times 1\] \[=16+8+0+2+1\] \[={{(27)}_{10}}\] \[\therefore \]Sum \[{{(100010)}_{2}}+{{(11011)}_{2}}\] \[={{(34)}_{10}}+{{(27)}_{10}}\] \[={{(61)}_{0}}\] Now,| 2 | 61 |
| 2 | 30-1 |
| 2 | 15-0 |
| 2 | 7-1 |
| 2 | 3-1 |
| 2 | 1-1 |
| 0-1 |
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