1. Number Systems & Logic Gates Day 2

2. Octal Number System Base (Radix)8 Digits0, 1, 2, 3, 4, 5, 6, 7 e.g.1623 8 1623 8 3 =5128 2 =648 1 =88 0 =1 The digit 2 in the second position from the right represents the value 16 and the digit 1 in the fourth position from the right represents the value 512.

3. Hexadecimal Number System Base (Radix)16 Digits0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F e.g.2F4D 16 2 F 4 D 16 3 =409616 2 =25616 1 =1616 0 =1 The digit F in the third position from the right represents the value 3840 and the digit D in the first position from the right represents the value 13.

4. Eg. 22 10 to Binary 10110 2 Conversions: Decimal to Binary (Integer) Remainder Divide integer until the integer quotient becomes 0 1 0 1 1 0 22 2 5 112 222 12 0

5. Eg. 10110 2 to Decimal 2 0 x 02 1 x 12 2 x 12 3 x 02 4 x 1 16 0 4 2 0 ++++ 22 1 0 1 1 0 Conversions: Binary to Decimal (Integer)

6. Eg. 135 10 to Octal 207 8 Conversions: Decimal to Octal (Integer) 0 7 2 168 1358 28 0

7. Eg. 207 8 to Decimal 2 0 7 8 0 x 78 1 x 08 2 x 2 64 2 0 7 ++ 135 x Conversions: Octal to Decimal (Integer)

8. D 9393 21116 338516 Eg. 3385 10 to Hexadecimal F E D 12 11 10 - - - 15-C 14-B 13-A D39 16 Conversions: Decimal to Hexadecimal (Integer) 1316 0

9. Eg. D39 16 to Decimal D 3 9 16 0 x 916 1 x 316 2 x 13 256 13 48 9 + + 3385 10 x F E D 12 11 10 - - - 15-C 14-B 13-A Conversions: Hexadecimal to Decimal (Integer)

10. Eg. 11001011101 2 to Octal 5 313 1 1 0 0 1 0 1 1 1 0 1 Conversions: Binary to Octal Therefore, 11001011101 2 = 3135 8

11. Eg. 3135 8 to Binary 101011001 11 3 13 5 Conversions: Octal to Binary Therefore, 3135 8 = 11001011101 2

12. Eg. 11001011101 2 to Hexadecimal D56 1 1 0 0 1 0 1 1 1 0 1 Conversions: Binary to Hexadecimal Therefore, 11001011101 2 = 65D 16

13. Eg. 65D 16 to Binary 11010101110 6 5D Conversions: Hexadecimal to Binary Therefore, 65D 16 = 11001011101 2

14. Logic Gates Binary information is represented in digital computers by physical quantities called signals. Two different electrical voltage levels such as 3 volts and 0.5 volts may be used to represent binary 1 and 0. Binary logic deals with binary variables and with operations that assume a logical meaning.

15. Logic Gates Contd.. A particular logic operation can be described in an algebraic or tabular form. The manipulation of binary information is done by the circuits called logic gates, which are blocks of hardware that produce signals of binary 1 or 0 when input logic requirements are satisfied.

16. Logic Gates Contd.. Each gate has a distinct graphics symbol and it’s operation can be described by means of an algebraic expression or in a form of a truth table. Each gate has one or more binary inputs and one binary output.

17. Logic Gates AND OR (Inclusive OR) NOT (inverter) NAND (Not AND) NOR (Not OR) XOR (Exclusive OR) XNOR (Exclusive NOR)

18. Logic Operations ANDLogic GateTruth Table A B x A B x 0 0 0 0 1 0 1 0 0 1 1 1 A, B Binary Input Variables x Binary Output Variable X=A.B

19. Logic Operations ORLogic GateTruth Table A B x 0 0 0 0 1 1 1 0 1 1 1 1 A B x X=A+B This is read as x equals A or B

20. Logic Operations NOT Logic GateTruth Table A x 0 0 1 1 x A X=A` X=A

21. Logic Operations NANDLogic GateTruth Table A B x 0 0 1 0 1 1 1 0 1 1 1 0 A B x X=A.B

22. Logic Operations NOR Logic GateTruth Table A B x 0 0 1 0 1 0 1 0 0 1 1 0 A B x X=A+B

23. Logic Operations XOR Logic GateTruth Table A B x 0 0 0 0 1 1 1 0 1 1 1 0 A B x

24. Logic Operations Exclusive-NOR Logic GateTruth Table A B x 0 0 1 0 1 0 1 0 0 1 1 1 A B x X= A + B