Answer to Question #315979 in Discrete Mathematics for Pravin

Question

Convert the following integers from decimal notation to binary notation.

a) 4532

b) 1023

Answer 1

a) To convert decimal number 4532 to binary, we follow these steps:

• Divide 4532 by 2 keeping notice of the quotient and the remainder.
• Continue dividing the quotient by 2 until you get a quotient of zero.
• Then just write out the remainders in the reverse order to get binary equivalent of decimal number 4532.

Using the above steps, here is the work involved in the solution for converting 4532 to binary number:

4532 / 2 = 2266 with remainder 0

2266 / 2 = 1133 with remainder 0

1133 / 2 = 566 with remainder 1

566 / 2 = 283 with remainder 0

283 / 2 = 141 with remainder 1

141 / 2 = 70 with remainder 1

70 / 2 = 35 with remainder 0

35 / 2 = 17 with remainder 1

17 / 2 = 8 with remainder 1

8 / 2 = 4 with remainder 0

4 / 2 = 2 with remainder 0

2 / 2 = 1 with remainder 0

1 / 2 = 0 with remainder 1

Then we just write down the remainders in the reverse order to get the answer, the decimal number 4532 converted to binary is therefore equal to :

1000110110100

b) Here is the work involved in the solution for converting 1023 to binary number:

1023 / 2 = 511 with remainder 1

511 / 2 = 255 with remainder 1

255 / 2 = 127 with remainder 1

127 / 2 = 63 with remainder 1

63 / 2 = 31 with remainder 1

31 / 2 = 15 with remainder 1

15 / 2 = 7 with remainder 1

7 / 2 = 3 with remainder 1

3 / 2 = 1 with remainder 1

1 / 2 = 0 with remainder 1

The decimal number 1023 converted to binary is equal to :

1111111111