1. Course Code 114 Introduction to Computer Science
Lecture 3
Number Systems and Conversions
Assoc. Prof. Hussam Elbehiery
Egypt 2018

4. Digital and Analogue
Two types of light control found in our homes: light switches and light dimmers.
A mercury thermometer is an analogue device since the mercury can creep up the tube reaching all values in turn.
Calendar is a digital device.

5. Digital system Vs. Binary systems
A digital system (not analogue) that has only two states is called a 'binary' system.
Digital electronics for control or decision-making circuits called 'logic circuits and the 1 and 0 conditions logic states.

6. Decimal system Base 10 numbering system.
“123”, How many items this value represents. The number 123 represents:
1* * *100 or
“ ”
1* * * *10–1 + 5*10–2 + 6*10–3

7. Binary Numbering System
Most modern digital systems operate using binary logic.
The digital systems represent values using two voltage levels (usually 0 v and +5 v).

8. Binary to Decimal Conversion
1*23 + 0*22 + 1*21 + 0*20 = = 1010

9. Decimal to Binary Conversion
Our final number is (10011)2

10. Binary Formats An eight-bit binary value uses bits 0 through 7:
X7 X6 X5 X4 X3 X2 X1 X0
A 16-bit binary value uses bit positions 0 through 15:
X15 X14 X13 X12 X11 X10 X9 X8 X7 X6 X5 X4 X3 X2 X1 X0

11. Bits: The smallest “unit” of data on a binary computer or digital system is a single bit. Bit, an abbreviation for Binary Digit.
Nibbles: A nibble is a collection of four bits.
Bytes: A group of eight bits is called a byte.

12. Word: A word is a group of 16 bits.
Double Word: D Word is a group of 32 bits.

13. Octal Numbering System
The octal number system uses base 8 instead of base 10 or base 2.
8 digits at our disposal, 0–7.
To convert 172 in octal to decimal:
Weight = 1*82 + 7*81 + 2*80
= 1*64 + 7*8 + 2*1 =
= 12210

14. 122/8 = 15 remainder 2 15/8 = 1 remainder 7 1/8 = 0 remainder 1 = 1728
Octal Binary

15. Hexadecimal Numbering System
The hexadecimal numbering system is the most common system seen today in representing raw computer data. Represent groups of 4 bits.
We have 16 symbols to use for digits The digits used in hex are the letters A, B, C, D, E, and F.

16. Decimal Binary Hexadecimal A B C D E F

17. To convert 15E in hex to decimal:
Weight = 1* * *160
= 1* * *1 = =
350/16 = 21 remainder 14 = E /16 = 1 remainder 5
1/16 = 0 remainder 1
So we get 15E for 350.

18. To convert AE to binary:
So AE in binary is

19. Assoc. Prof. Hussam Elbehiery
Thank you
With all my best wishes
Assoc. Prof. Hussam Elbehiery