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Computer Science

Convert decimal number into binary number.

(a) 52

(b) 44

(c) 25.80

(d) 62.325

Number System

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Answer

(a) 52

252Remainder
2260 (LSB)
2130
261
230
211
 01 (MSB)

Therefore, (52)10 = (110100)2.

(b) 44

244Remainder
2220 (LSB)
2110
251
221
210
 01 (MSB)

Therefore, (44)10 = (101100)2.

(c) 25.80

Let us first convert 25 into binary as shown below:

225Remainder
2121 (LSB)
260
230
211
 01 (MSB)

The binary equivalent of integer part (25)10 = (11001)2.

Now let us convert (0.80)10 into binary as shown below:

Multiply=IntegerFraction
0.80 x 2=10.6 (MSB)
0.6 x 2=10.2
0.2 x 2=00.4
0.4 x 2=00.8
0.8 x 2=10.6 (LSB)

The binary equivalent of fractional part (0.8)10 = (11001)2.

Therefore, (25.80)10 = (11001.11001)2.

(d) 62.325

Let us first convert 62 into binary as shown below:

262Remainder
2310 (LSB)
2151
271
231
211
 01 (MSB)

The binary equivalent of integer part (62)10 = (111110)2.

Now let us convert (0.325)10 into binary as shown below:

Multiply=IntegerFraction
0.325 x 2=00.65 (MSB)
0.65 x 2=10.3
0.3 x 2=00.6
0.6 x 2=10.2
0.2 x 2=00.4
0.4 x 2=00.8
0.8 x 2=10.6 (LSB)

The binary equivalent of fractional part (0.325)10 = (0101001)2.

Therefore, (62.325)10 = (111110.0101001)2.

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