NTA UGC NET JUNE-2023 Paper-2

We convert the whole number and fractional parts separately and then combine the results.

WHOLE NUMBER PART

The whole number part of 3.72 is 3. Divide this number repeatedly by 2 until the quotient becomes 0.
When 3 is divided by 2, the quotient is 1 and the remainder is 1.
When 1 is divided by 2, the quotient is 0 and the remainder is 1.
Write the remainders from bottom to top.

(3)10 = (11)2

FRACTIONAL PART

The fractional part of 3.72 is 0.72. Multiply the fractional part repeatedly by 2 until it becomes 0. Stop after a number of steps if the fractional part does not become 0.

0.72 × 2 = 1.44
0.44 × 2 = 0.88
0.88 × 2 = 1.76
0.76 × 2 = 1.52
0.52 × 2 = 1.04
0.04 × 2 = 0.08
0.08 × 2 = 0.16
0.16 × 2 = 0.32
…………
From top to bottom, write the integer parts of the results to the fractional part of the number in base 2.

(0.72)10 = (0.10111000…)2

OVERALL RESULT

Combine the whole number and fractional parts to obtain the overall result.

(3.72)10 = (11)2 + (0.10111000…)2 = (11.10111000…)2