# How to Convert Negative Numbers to Binary

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Because the binary number system has only two symbols--1 and 0--representing negative numbers is not as simple as adding a minus sign in front. There are, however, simple ways to represent a negative number in binary. This article will offer three solutions to that problem.

## Use a Sign Bit

Select the number of bits you will use to represent your binary numbers. An eight-bit number has been long used as a standard. It was the original size for an integer in computer programming. Of course, there are also long integers (16 bits). Note: if you use an eight-bit integer, then only seven bits will be used to represent your actual number.

Select the leftmost bit to serve as a sign bit. If the bit is 0, the number is positive. If it is 1, the number is negative.

Write your negative number using all eight bits. Therefore the number -5 would be written as 10000101.

## Using 1s Compliment

Write the number in binary as you would if it were positive. Again, write 5 as 00000101, assuming we are using eight-bit integers.

Invert the digits--i.e. 1s go to 0s and 0s go to 1s. Therefore, 5 becomes 11111010.

Use the leftmost bit as the sign bit. So just as with using a sign bit, positive numbers will all have a 0 leading bit (when written in an 8 bit format) while all negative numbers will contain a leading 1. To use the number, use the sign bit information and flip the digits back for numerical value.

## Using 2s Compliment

Write the number as you would as if it were positive, using all eight bits. So 5 is 00000101.

Invert the bits, switching the 1s and 0s as you did with 1s compliment. So, again, 5 becomes 11111010.

Add 1 to your number. So 5 becomes 11111010 + 00000001 = 11111011.

Check your answer. The number 11111011 would be, converted back to base 10: -128 + 64 + 32 + 16 + 8 + 0 + 2 + 1 = -5.

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