See how Convert the decimal numbers 1987 to binary then to octal?

Answer 1

to convert decimal to binary, repeatedly divide the value by 2, taking the remainder until the value is 1 or 0.

1987 / 2 = 993 r 1

993 / 2 = 496 r 1

496 / 2 = 248 r 0

248 / 2 = 124 r 0

124 / 2 = 62 r 0

62 / 2 = 31 r 0

31 / 2 = 15 r 1

15 / 2 = 7 r 1

7 / 2 = 3 r 1

3 / 2 = 1 r 1

1 / 1 = 1

Thus: 1987 in binary is 11111000011.

Proof (binary back to decimal):

1 * 2^0 = 1

1 * 2^1 = 2

0 * 2^2 = 0

0 * 2^3 = 0

0 * 2^4 = 0

0 * 2^5 = 0

1 * 2^6 = 64

1 * 2^7 = 128

1 * 2^8 = 256

1 * 2^9 = 512

1 * 2^10 = 1024

1024 + 512 + 256 + 128 + 64 + 2 + 1 = 1987

To convert to octal, split the binary value into groups of 3 bits:

11 111 000 011

Pad the first group with zeroes to make 3 bits if necessary:

011 111 000 011

Convert each group to its equivalent octal digit according to the following table:

000 = 0

001 = 1

010 = 2

011 = 3

100 = 4

101 = 5

110 = 6

111 = 7

Therefore: 011 111 000 011 = 3 7 0 3

Thus: 1987 in octal is 3703.

Proof:

3 * 8^0 = 3

0 * 8^1 = 0

7 * 8^2 = 448

3 * 8^3 = 1536

1536 + 448 + 3 = 1987