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Convert decimal integers to binary, octal, and hexadecimal.

Mathematics

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Answers

3 parts
a

1110012111001_2

b

11511811511_8

c

CFF916CFF9_{16}

Step-by-step solution

15 steps

Here are the solutions to your questions.

QUESTION ONE

Part a· 6 steps

Convert 571057_{10} into binary

To convert a decimal integer to binary, we repeatedly divide the decimal number by 2 and record the remainders. We then read the remainders from bottom to top.

  1. Divide 57 by 2.

    57÷2=2857 \div 2 = 28 R 1

  2. Divide 28 by 2.

    28÷2=1428 \div 2 = 14 R 0

  3. Divide 14 by 2.

    14÷2=714 \div 2 = 7 R 0

  4. Divide 7 by 2.

    7÷2=37 \div 2 = 3 R 1

  5. Divide 3 by 2.

    3÷2=13 \div 2 = 1 R 1

  6. Divide 1 by 2.

    1÷2=01 \div 2 = 0 R 1

    Reading the remainders from bottom to top gives the binary equivalent.

    5710=111001257_{10} = \boxed{111001_2}

Part b

11511811511_8

Convert 4937104937_{10} into octal

To convert a decimal integer to octal, we repeatedly divide the decimal number by 8 and record the remainders. We then read the remainders from bottom to top.

  1. Divide 4937 by 8.

    4937÷8=6174937 \div 8 = 617 R 1

  2. Divide 617 by 8.

    617÷8=77617 \div 8 = 77 R 1

  3. Divide 77 by 8.

    77÷8=977 \div 8 = 9 R 5

  4. Divide 9 by 8.

    9÷8=19 \div 8 = 1 R 1

  5. Divide 1 by 8.

    1÷8=01 \div 8 = 0 R 1

    Reading the remainders from bottom to top gives the octal equivalent.

    493710=1151184937_{10} = \boxed{11511_8}

Part c

CFF916CFF9_{16}

Convert 532411053241_{10} into hexadecimal

To convert a decimal integer to hexadecimal, we repeatedly divide the decimal number by 16 and record the remainders. Remainders 10-15 are represented by letters A-F. We then read the remainders from bottom to top.

  1. Divide 53241 by 16.

    53241÷16=332753241 \div 16 = 3327 R 9

  2. Divide 3327 by 16.

    3327÷16=2073327 \div 16 = 207 R 15 (which is F in hexadecimal)

  3. Divide 207 by 16.

    207÷16=12207 \div 16 = 12 R 15 (which is F in hexadecimal)

  4. Divide 12 by 16.

    12÷16=012 \div 16 = 0 R 12 (which is C in hexadecimal)

    Reading the remainders from bottom to top gives the hexadecimal equivalent.

    5324110=CFF91653241_{10} = \boxed{CFF9_{16}}

Part d

Convert 511.8062510511.80625_{10} into binary

This conversion involves two parts: the integer part and the fractional part.

  • Integer Part (51110511_{10} to binary): Repeatedly divide the integer part by 2 and record the remainders. 511÷2=255511 \div 2 = 255 R 1 255÷2=127255 \div 2 = 127 R 1 127÷2=63127 \div 2 = 63 R $
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