Negative Decimal to Binary Converter

Negative Decimal to Binary Converter

FAQs

To convert negative decimals to binary, particularly using two's complement representation, follow these steps:

1. Convert the absolute value of the negative decimal number to its binary representation.
2. Pad the binary number with leading zeros to make it the desired bit length if necessary.
3. Invert (flip) all the bits (change 0s to 1s and 1s to 0s) in the binary representation obtained in step 1.
4. Add 1 to the inverted binary number.

Here are some examples:

Example 1: Convert -7 to binary using 8 bits (two's complement):

1. Absolute value of -7 is 7, which is 111 in 3 bits.
2. Pad with leading zeros: 00111.
3. Invert the bits: 11000.
4. Add 1: 11001.

So, the binary representation of -7 in two's complement using 8 bits is 11001.

Example 2: Convert -10 to binary using 8 bits (two's complement):

1. Absolute value of -10 is 10, which is 1010 in 4 bits.
2. Pad with leading zeros: 00001010.
3. Invert the bits: 11110101.
4. Add 1: 11110110.

So, the binary representation of -10 in two's complement using 8 bits is 11110110.

Note: The bit length used for two's complement representation determines the range of representable negative values. For n bits, you can represent values in the range from -2^(n-1) to 2^(n-1) - 1.

Negative numbers are indeed represented in binary using two's complement to enable arithmetic operations like addition and subtraction.