Convert the decimal expansion of each of these integers to a binary expansion. a) 321
b) 1023
c) 100632

Step-by-step explanation:

Given

a) 321

b) 1023

c) 100632

Required

Convert to decimal

To convert each of these to binary, we have to divide the quotient by 2 and we take note of the remainder;

Solving (a)

321 / 2 = 160 R 1

160 / 2 = 80 R 0

80 / 2 = 40 R 0

40 / 2 = 20 R 0

20 / 2 = 10 R 0

10 / 2 = 5 R 0

5 / 2 = 2 R 1

2 / 2 = 1 R 0

1 / 2 = 0 R 1

Hence;

Solving (b)

1023 / 2 = 511 R 1

511 / 2 = 255 R 1

255 / 2 = 127 R 1

127 / 2 = 63 R 1

63 / 2 = 31 R 1

31 / 2 = 15 R 1

15 / 2 = 7 R 1

7 / 2 = 3 R 1

3 / 2 = 1 R 1

1 / 2 = 0 R 1

Hence;

Solving (c)

100632 / 2 = 50316 R 0

50316 / 2 = 25158 R 0

25158 / 2 = 12579 R 0

12579 / 2 = 6289 R 1

6289 / 2 = 3144 R 1

3144 / 2 = 1572 R 0

1572 / 2 = 786 R 0

786 / 2 = 393 R 0

393 / 2 = 196 R 1

196 / 2 = 98 R 0

98 / 2 = 49 R 0

49 / 2 = 24 R 1

24 / 2 = 12 R 0

12 / 2 = 6 R 0

6 / 2 = 3 R 0

3 / 2 = 1 R 1

1 / 2 = 0 R 1

Hence;

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