How are negative numbers represented in Binary? | The Signed bit. | DE.03


Till now any numbers we came across
in previous videos were positive real numbers. But negative numbers also exist, so should their representation in binary. This brings us to signed magnitude representation. This representation is capable of handling
both the positive and negative numbers. An extra sign bit at MSB position is added
to a regular binary number to represent in sign magnitude form. Bit 0 at MSB represents positive number with
remaining bits for its magnitude. Bit 1 at MSB represents negative number and remaining bits represent the magnitude. The number 00101 in sign magnitude form represents +5. The number 10011 in sign magnitude form represents -3. The next representation is 1’s complement. This representation is achieved by replacing
0 with 1 and 1 with 0 of any binary number. The 1’s complement of 00110 is 11001. The number obtained after switching the bits of original number is complement of the first number. This method widely represents signed numbers. 0011 represents +3. It’s 1’s complement 1100 represents -3. Here, 0 at MSB indicates positive and 1 at MSB indicates negative binary number. Let us find +6 and -6 in 1’s complement
form. The next representation is Two’s complement form. It is obtained by adding 1 to 1’s complement form. Consider +5, it’s binary is 0101 , it’s 1’s complement form is 1010 and it’s 2’s complement form is 1011. There is a shortcut to finding 2’s complement directly from the original without the need to calculate 1’s complement form. The method is to scan the original binary
from LSB towards MSB and copy all the digits till first 1 occurs. After this bit, just complement all the higher bits. Let us see some examples.

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