**APPENDIX D**

**Representing Negative Integers**

The industry standard method for representing negative integers is called **two’s complement**. Here is how it works:

For an integer represented using 16 bits, the leftmost bit is reserved for the sign bit. If the sign bit is 0, then the integer is positive; if the sign bit is 1, then the integer is negative.

For example, let’s consider two numbers, one positive and one negative.

0000 0101 0111 1001 is a positive integer, which we call *a*.

1111 1111 1101 1010 is a negative integer, which we will call *b*.

Using the methodology presented in Chapter 1 for converting a binary number to a decimal number, we can convert the binary number, *a*, to its decimal equivalent. Hence, the value of *a* is calculated as follows: ...

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