Question

Convert (-6), (-27), (-64) to binary number system?Convert (-6), (-27), (-64) to binary number system?

Answer 1

There are several ways to represent these negative numbers in binary, but first let's convert them into their corresponding positive numbers:

6₁₀=110₂, 27₁₀=11011₂, 64₁₀=1000000₂ where the subscript shows the number base.

-6=-110, -27=-11011, -64=-1000000 is the mathematical way of representing the binary.

Another way is to use the "complement plus 1". In this system, -1 is represented by "all 1s:

11...111 so 11...111-110+1=11...001+1=11...010. In a 24-bit system we would have:

111111111111111111111010. So the number of leading 1s depends on the word capacity of the number, and if we use a byte as 8 bits the representation of -6 would be 11111010. When this is added to 110 (=6₁₀) we get the byte 00000000, representing zero. 

If we use the byte method then -27=11100101₂ and -64=11000000₂. For 8-bit bytes the negative is effectively 256-n where n is the number.

For example, -27=256-27=229=224+5=7×32+5=11100101₂. For larger word representations simply write the required number of leading 1s.