Binary equivalent of five – UGC NET Question

To convert decimal 5 to binary, we express 5 as a sum of powers of 2. Here 5 equals 4 + 1, which corresponds to 2^2 and 2^0. This gives the binary pattern 101, with bits for 4, 0 and 1 respectively. Therefore, 101 (base 2) is the correct binary representation of 5.

Option A:
Option A is correct because it places a 1 in the 4's place and a 1 in the 1's place, giving 4 + 1 = 5. The middle bit is 0, indicating there is no contribution from the 2's place. This matches the required decimal value exactly.

Option B:
Option B represents 100 in binary, which corresponds to 4 and not 5. It has a 1 only in the 4's place and zeros elsewhere. Since 4 is smaller than 5, this cannot be the correct equivalent.

Option C:
Option C gives 111 in binary, which equals 4 + 2 + 1 = 7. This is larger than the required value of 5. Therefore 111 (base 2) does not represent decimal 5.

Option D:
Option D shows 110 in binary, which is 4 + 2 = 6. This is again not equal to 5, so it cannot be the correct binary representation.