Binary Logic
- 1. Two Choices Why computers use binary
- 2. Why binary? Electronic computers use electricity to represent real information. This is similar to an electric light switch. When the switch is in the “on” position, the light will be on. When it is the “off” position, the light will be off. On a computer we can store this information as a single number. 1 would mean that the light is on. 0 would mean that the light is off. 14/11/2013 2
- 3. Bits, Nibbles and Bytes Computers store millions of pieces of binary information – we need a way of grouping them together! A single binary digit is called a “bit”. This stands for binary digit. 14/11/2013 3
- 4. Units The smallest unit in binary is the bit. Four bits together are called one nibble. Eight bits are called one byte. 1024 bytes are called one kilobyte (kb) 1024 kilobytes are called one megabyte (mb) 1024 megabytes are called one gigabyte (gb) 1024 gigabytes are called one terabyte (tb) 14/11/2013 4
- 5. How many values One bit can store two values (0 and 1) How many different ways can we arrange two bits in? 00 01 10 11 Two bits give four different values 14/11/2013 5
- 6. Nibbles Four bits together (half a byte), is called a nibble On your worksheet (Activity 1), write all the different values that we can store in one nibble. Warning – Maths ahead! 1 bit can store 21 values (2 different value) 2 bits can store 22 values (4 different values) 3 bits can store 23 values (8 different values) 4 bits can store 24 values (16 different values) How many values in 5 bits? 14/11/2013 6
- 7. One nibble 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 14/11/2013 There are 16 different values that can be stored in one nibble Can you see a pattern? 7
- 8. One nibble 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 14/11/2013 In the right column, the zero and one swap every time 8
- 9. One nibble 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 14/11/2013 In the second column, the zero and one are on for two values, then off for two values. 9
- 10. One nibble 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 14/11/2013 In the third column, the ones and zeros are on for four values, then off for four values. 10
- 11. One nibble 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 14/11/2013 In the fourth column, the ones are on for eight values and off for eight values. 11
- 12. Convert them to “denary” 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 14/11/2013 Zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (1 x 1) (1 x 2 + 0 x 1) (1 x 2 + 1 x 1) (1 x 4 + 0 x 2 + 0 x 1) (1 x 4 + 0 x 2 + 1 x 1) (1 x 4 + 1 x 2 + 0 x 1) (1 x 4 + 1 x 2 + 1 x 1) (1 x 8 + 0 x 4 + 0 x 2 + 0 x 1) (1 x 8 + 0 x 4 + 0 x 2 + 1 x 1) (1 x 8 + 0 x 4 + 1 x 2 + 0 x 1) (1 x 8 + 0 x 4 + 1 x 2 + 1 x 1) (1 x 8 + 1 x 4 + 0 x 2 + 0 x 1) (1 x 8 + 1 x 4 + 0 x 2 + 1 x 1) (1 x 8 + 1 x 4 + 1 x 2 + 0 x 1) (1 x 8 + 1 x 4 + 1 x 2 + 1 x 1) 12
- 13. Activity sheet Please do activities two and three on the sheet 14/11/2013 13
- 14. Binary addition + 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 + 0 + 1001011011=inin binary. We write 1 + 1 is is 2 which is 1045 denary write 2 + 0 + 1is 10so we write 0 which is binary. We 0 1 1 0 is 1 we can write that answer below 1 + 0 is 1 soso we write 1 in the box below 0+1 0 0 0 inin the1 in the boxand carry 1 0 the box below and carry denary box below below 10000110 = 134 1 10110011 = 179 denary 14/11/2013 14
- 15. Activity 4 Some examples of binary addition are in activity 4 14/11/2013 15
- 16. Binary Logic As well as adding binary numbers we can also use “Binary Logic” The three “operations” that we need to know are AND OR NOT 14/11/2013 16
- 17. AND The rule that we apply with “AND” is that both bits need to be a 1 to give the answer of 1 0 1 0 1 14/11/2013 AND = AND 0 0 1 = 0 0 0 AND 1 = 1 AND = 17
- 18. OR The rule that we apply with “OR” is that either bit can be a 1 to give the answer of 1 = 0 OR 0 0 = 1 OR 0 1 = 0 OR 1 1 1 14/11/2013 OR 1 = 1 18
- 19. NOT NOT simply reverses the zero and ones NOT NOT 0 1 = = 1 0 Now complete Activity 5 14/11/2013 19
- 20. Nightclub Activity 6 Come and visit Yorkshire’s number one nightclub Mondays only No Alcohol night, so you don’t need proof of age, and no dress code! 14/11/2013 20
- 21. AND and OR in computers So how does this binary help a computer? We can use bits to store whether a customer has met the requirements. VIP Monday Proof of Age No Denim No Trainers 1 1 1 1 1 If either of these are 1 = Allowed in (OR) 14/11/2013 All of these have to be 1 = Allowed in (AND) 21
- 22. Truth Tables In your exam, you may be asked to complete a “truth table” For example, what is the truth table for P = A AND B Page 39 in text book 14/11/2013 22
- 23. Logic Symbols A Has two inputs C B And one output A 0 C 0 0 1 0 1 0 0 1 14/11/2013 B 0 1 1 23
- 24. Logic Symbols A Has two inputs C B And one output A 0 C 0 0 1 1 1 0 1 1 14/11/2013 B 0 1 1 24
- 25. Logic Symbols Activity 7 – just first three questions Activity 7 – questions four, five, six Now the tricky ones – try the rest 14/11/2013 25