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 numeral,. The given number is first converted from binary to decimal equivalence \[{{(100010)}_{2}}={{2}^{5}}\times 1+{{2}^{4}}\times 0+{{2}^{3}}\times 0\] \[+{{2}^{2}}\times 0+{{2}^{1}}\times 1+{{2}^{0}}\times 0\] \[=32+0+0+2+0\] \[+{{(34)}_{10}}\] and \[{{(11011)}_{2}}={{2}^{4}}\times 1+{{2}^{3}}\times 1\] \[+{{2}^{2}}\times 0+{{2}^{1}}\times 1+{{2}^{0}}\times 1\] \[=16+8+0+2+1\] \[{{(27)}_{10}}\] \[\therefore \] Sum \[{{(100010)}_{2}}\text{ }+\text{ (}11011{{\text{)}}_{2}}\] \[{{(34)}_{10}}+{{(27)}_{10}}\] \[={{(61)}_{10}}\] Now,| 2 | 61 |
| 2 | 30 - 1 |
| 2 | 15 - 0 |
| 2 | 7 - 1 |
| 2 | 3 - 1 |
| 2 | 1 - 1 |
| 0 - 1 |
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