Number system

Introduction
Conversions

1. Bilquis Post Graduate College Woman Topic:                                     " Number System "  Submitted To:                                       Sir Waqas Submitted By:                                       Sana Waheed                                       Hira Kanwal                                        Sunila Sheikh                                       Samreen Yousaf Submission Date:                                       18, Decemeber 2018

2. NUMBER SYSTEM

3. NUMBER SYSTEM        Number system is used to represent information in quantitative(determinable) form.        TYPES OF NUMBER SYSTEM:         Number system is further divided into following parts:  DECIMAL NUMBER SYSTEM  BINARY NUMBER SYSTEM  OCTAL NUMBER SYSTEM  HEXADECIMAL NUMBER SYSTEM

4. DECIMAL NUMBER SYSTEM Decimal number system has  ten-digits represented by (0-9). Any decimal number can be represented by these digits and since there are 10 digits ,therefore  the base of this number system is 10.

5. BINARY NUMBER SYSTEM In Binary Number system, we have two digits (0 and 1) .  Computer represents all kinds of data and information in binary number it includes audio, graphic etc. The base of binary number system is 2. 

6. OCTAL NUMBER SYSTEM An Octal Number System has eight   digits represented as (0-7) i.e. digits 0,1,2,3,4,5,6. The base of octal number system is 8.

7. HEXA-DECIMAL NUMBER SYSTEM The Hexa-Decimal System has 16 digits, which are represented as 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F The base of hexadecimal number system is 16.

8. CONVERSION-I

9. CONVERSION OF DECIMAL TO OTHER NUMBER SYSTEM Decimal to Binary Number System E.g. (42) 10 2 42 2 21-0 2 10-1 2 5-0 2 2-1 2 1-0 (42) 10 = (101010) 2 Decimal to Octal Number System E.g. (952) 10 8 952 8 119-0 8 14-7 8 1-6 8 0-1 (952) 10 =(1670) 8

10. To be Continued! Decimal into Hexa –Decimal E.g. (428) 10 16 428 16 26-12 16 1-10 0-1 (428) 10 = (1AC) 16

11. OTHER NUMBER SYSTEM INTO DECIMAL NUMBER SYSTEM Binary Into Decimal Number System E.g. (11001) 2 11001=1x2 4 +1x2 3 +0x2 2 +0x2 1 +1x2 =1x16+1x8+0x4+0x2+1x1 =16+8+0+0+1 =25 =(25) 10 Octal Into Decimal Number System E.g. (211) 8 211=2x8 2 +1x8 1 +1x8 =2x16+1x8+1x1 =128+8+1 =137 =(137) 10

12. To Be Continued! Hexa-decimal Into Decimal Number System E.g. (DF) 16 DF = 13x16 1 +15x16 =13x16+15x1 =208+15 =223 =(223) 10

13. CONVERSION-II

14. OTHER SYSTEM TO OTHER NUMBER SYSTEM Converting from base other than ‘10’ to another base other than ‘10’: Following are the  steps for base conversions: Convert the original number to base (10) decimal. Convert the decimal number to required base number.

15. EXAMPLES: Example No.01: (545)6=?4 STEP-1 545 6  5x6 + 4x6 + 5x6  5x36 +4x6 + 5x1 180 + 24 + 5 =(209)10 STEP-2 4 209 4 52-1 4 13-0 4 3 -1 0 -3 (545)6 = (3101)4  

16. EXAMPLES: Example No.02: (11010011)2 = ?16 STEP-1: =1x2+1x2+0x2+1x2+0x2+0x2+1x2+1x2 =1x128+1x64+0x32+1x16+0x8+0x4+1x2+1x1 =128+64+0+16+8+4+2+1 =(211)10 STEP-2: 16 211 16 13-3 0-13 (11010011)2 = (D3)16

17. CONVERSION-III

18. CONVERSION OF BINARY NUMBER SYSTEM TO OTHER NUMBER SYSTEM BINARY TO DECIMAL PROCESS: In order to convert binary number system into decimal number system we should follow following steps:- Multiply each bit of the Binary Number by it corresponding bit-weighting factor (i.e. Bit-0→2=1; Bit-1→21=2; Bit-2→22=4; etc.). Sum up all the products  to get the Decimal Number.  

19. BINARY TO DECIMAL NUMBER SYSTEM ∴   0110 2 =  6 10 EXAMPLE:1 Convert binary number 0110 2 into decimal equivalent?

20. BINARY TO DECIMAL NUMBER SYSTEM EXAMPLE:2 Convert binary number 0110101 2 into decimal equivalent.

21. BINARY TO OCTAL NUMBER SYSTEM PROCESS : In order to convert binary number system octal number system we should follow following steps:- Take the binary number and from right to left, group all place holders in triplets. Add leading zeros , if     necessary                             10001100101001 2      010     001     100    101      001

22. BINARY TO OCTAL NUMBER SYSTEM Convert each triplet to its single-digit octal equivalent.              010 001 100 101 001 2  =                      010      001    100      101    001               2           1        4         5        1

23. BINARY TO HEXADECIMAL NUMBER SYSTEM Sometimes, it is necessary to use a numbering system that has more than ten base digits. One such numbering system, hexadecimal, is useful on the Web. Hexadecimal number, a Base-16 numbering system, is used in specifying web colors.

24. BINARY TO HEXADECIMAL NUMBER SYSTEM There are new symbols for the base-16 equivalent of the base-10 number 10,11,12,14 and 15.

25. The End 🌷  Thanks! For Your Attention