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Convert the following decimal values into their binary equivalent in a 16-bit 1's complement representation. Do not use spaces, punctuation or symbols in your answer. The first conversion has been done for you. Decimal 16-bit 1's Complement -25 2048 -498 -50 -12345

Question

Convert the following decimal values into their binary equivalent in a 16-bit 1's complement representation. Do not use spaces, punctuation or symbols in your answer. The first conversion has been done for you.

Decimal 16-bit 1's Complement -25 2048 -498 -50 -12345

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Solution

To convert decimal values into their binary equivalent in a 16-bit 1's complement representation, you need to follow these steps:

  1. Convert the absolute value of the decimal number to binary.
  2. If the decimal number is positive, the binary equivalent in 16-bit 1's complement is the same as the binary number obtained in step 1, padded with zeros at the left to make it 16 bits.
  3. If the decimal number is negative, the binary equivalent in 16-bit 1's complement is obtained by inverting all the bits of the binary number obtained in step 1, padded with zeros at the left to make it 16 bits.

Let's apply these steps to the decimal numbers given:

-25:

  1. The binary of 25 is 11001.
  2. Since -25 is negative, we invert the bits to get 00110.
  3. Pad with zeros to make it 16 bits: 1111111111110010.

2048:

  1. The binary of 2048 is 100000000000.
  2. Since 2048 is positive, we don't need to invert the bits.
  3. Pad with zeros to make it 16 bits: 0000100000000000.

-498:

  1. The binary of 498 is 111110010.
  2. Since -498 is negative, we invert the bits to get 000001101.
  3. Pad with zeros to make it 16 bits: 1111111110001101.

-50:

  1. The binary of 50 is 110010.
  2. Since -50 is negative, we invert the bits to get 001101.
  3. Pad with zeros to make it 16 bits: 1111111111101101.

-12345:

  1. The binary of 12345 is 11000000111001.
  2. Since -12345 is negative, we invert the bits to get 00111111000110.
  3. Pad with zeros to make it 16 bits: 1111001111100010.

This problem has been solved

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