云南农业大学计算机导论课件Chapter4 Operations on Bits.pptVIP

4.1 ARITHMETIC OPERATIONS ARITHMETIC OPERATIONS ON INTEGERS Addition in Two’s Complement Adding numbers in two’ s complement is like adding the numbers in decimal; you add column by column, and if there is a carry, it is added to the next column. When you add 2 bits, the result is 0 or 1. Overflow Overflow is an error that occurs when you try to store a number that is not within the range defined by the allocation. When you add numbers in two’s complement using N bits, make sure that each number and the result are in the range defined for two’s complement representation. Subtraction in Two’s Complement One of the advantages of two’s complement representation is that there is no difference between addition and subtraction. To subtract, negate (two’s complement) the second number and add. In other words, the following two statements are the same: Number 1 – Number 2 ?? Number 1 + (-Number 2) 4.2 LOGICAL OPERATIONS A single bit can be either 0 or1.You can interpret 0 as the logical value false and 1 as the logical value true. A logical operation can accept 1 or 2 bits to create only 1 bit. If the operation is applied to only one input, it is a unary operation, if it is applied to 2 bits, it is a binary operation. TRUTH TABLES One way to show the result of a logical operation is with a truth table. A truth table lists all the possible input combinations with the corresponding output. UNARY OPERATOR NOT Operator The NOT operator has one input (a bit pattern). It inverts bits; that is, it changes 0 to1 and 1 to 0. BINARY OPERATORS AND Operator It takes two inputs (two bit patterns) and creates one output (bit pattern). For each pair of input bits, the result is 1 if and only if both bits are 1; otherwise, it is 0. Inherent Rule of the AND Operator One interesting point about the AND operator is that if a bit in one input is 0, you do not have to check the corresponding bit in the other input, you can qu