Bits, Data types, and Operations: Chapter 2

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

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 2nrows • The n columns refer to the source operands and the +1 refers to the output • Each value has two possible values, so there are 2n choices

6. AND Function

7. AND Function

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

15. OR Function

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

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

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!