1. Bits, Data types, and Operations: Chapter 2 COMP 2610 Dr. James Money COMP 2610 1

2. Operations on Bits So far, we have seen we can perform addition and subtraction on binary patterns Recall the meaning of ALU – arithmetic and logic unit The other set of operations is logical operations

3. Operations on Bits Recall that the name logical is historical in origin It refers to the fact that a bit has two values 0 and 1 These refer to false and true, respectively We consider several basic logical functions of the ALU

4. AND Function AND is a binary logical function It takes two source operands, and produces one result Each source is a logical values, either 0 or 1 The output of AND is 1 only if both the source values are 1 Otherwise the output is 0

5. AND Function A convenient way to represent the behavior of logical operation is the truth table A truth table has n+1 columns and 2 n rows The n columns refer to the source operands and the +1 refers to the output Each value has two possible values, so there are 2 n choices

6. AND Function ABAND 000 010 100 111

7. AND Function AND10 110 000 TrueFalse True False

8. AND Function We can also apply the AND operation to two bits patterns of m bits each We apply the AND function to each pair of bits in the two source operands This operation is called a bitwise AND

9. AND Function IF c=a AND b where a=0011101001101001 and b=0101100100100001, what is c? a: 0011101001101001 b: 0101100100100001 c: 0001100000100001

10. AND Function Suppose we have an 8 bit pattern called A in which only the two right-most bits are significant The computer will do one of four tasks depending on the value of these two bits How do we isolate these two bits?

11. AND Function We can use a bitmask to get this value The bitmask should be 1 for the bits you are interested in and 0 elsewhere So we would use the bitmask 00000011 Then we apply the A AND bitmask

12. AND Function If A=01010110, A:01010110 Bitmask:00000011 00000010 If A=11111100, A:11111100 Bitmask:00000011 00000000

13. OR Function OR is also a binary logical function It requires two source operand and produces one output The output of OR is only 0 if both inputs are 0 Otherwise, it is 1 We can apply the OR operation to m bits the same as the AND function

14. OR Function ABOR 000 011 101 111

15. OR Function OR10 111 010 ANDTrueFalse True FalseTrueFalse

16. OR Function Some times this is called the inclusive-OR function to differentiate it from the exclusive OR operator Let a=0011101001101001 and b=0101100100100001 What is c=a OR b?

17. OR Function a: 0011101001101001 b: 0101100100100001 c:0111101101101001

18. NOT Function NOT is a unary logical function That is, it only takes one source operand, and outputs one result This is also known as the complement operation We says the output is formed by inverting the bits

19. NOT Function ANOT 01 10

20. NOT Function We can apply the NOT function to a single m bit pattern the same way we apply it to two m bit patterns for AND and OR Let c=NOT a and a=0011101001101001 a: 0011101001101001 c:1100010110010110

21. XOR Function The Exclusive-OR or XOR function is a binary logical function with two source operands and one result The output of XOR is 1 two sources are different Otherwise, the output is 0 We can apply this to m bit patterns as well

22. XOR Function ABXOR 000 011 101 110

23. XOR Function Let a=0011101001101001, b=01011001001000001, and find c=a XOR b a:0011101001101001 b: 0101100100100001 c:0110001101001000 We can use XOR to determine if two bit patterns are identical!