Chapter 8 - Binary Arithmetic

Abstract

Unsigned binary numbers don’t have the concept of a sign (plus or minus), which means they can be used to represent only positive values. Each “ x ” character represents a single bit; the right-hand bit is known as the Least Significant Bit (LSB) because it represents the smallest value. Two unsigned binary numbers may be added together using a process identical to that used for decimal addition. First, the two least significant bits are added together to give a sum and, possibly, a carry-out to the next stage. This process is repeated for the remaining bits, progressing toward the most significant. In the case of binary (base-2) numbers, the radix complement is known as the twos’ complement and the diminished radix complement is known as the ones’ complement. Once again, the standard way of performing the operation would be to subtract the subtrahend (00011110 2) from the minuend (00111001 2), which may require the use of one or more borrow operations. In standard decimal arithmetic, numbers are typically represented in a form known as sign-magnitude, which means prefixing values with plus or minus signs (by default, numbers without signs are assumed to represent positive values). Signed binary numbers have the concept of a sign, and they can be used to represent both positive and negative values. The end result of using signed binary numbers is to greatly reduce the complexity of operations within a computer. Binary numbers may be multiplied together by means of a shift-and-add technique.