Number Base System
Number Base System
A number base system is the collection of symbols and rules for representing both small and large numbers. There are many number systems used today, some are examined below.
Types of Number Base Systems
Binary Number System
The Binary Number System is the number system in base 2. There are only two symbols (digits) in this system, which are 0 and 1.
Octal Number System
Octal or Oct means eight (8). Hence, the Octal Number System is a number system in base 8. There are eight (8) symbols used in this system: 0, 1, 2, 3, 4, 5, 6, and 7.
Decimal or Denary Number System
Decimal Number System is base ten (10). Ten symbols are used in this system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This is the system we use for everyday counting.
Hexadecimal Number system
Hex and decimal represent 6 and 10 respectively, making the Hexadecimal Number System a base 16 system. The sixteen symbols used are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. It is important to note that letters A, B, C, D, E and F represent the decimal values of 10, 11, 12, 13, 14 and 15 respectively.
Conversion From One Number Base System To Another
Binary to Decimal Number Conversion
To convert from binary to Decimal, multiply each binary digit by an increasing power (right to left) of 2 and sum the results.
Solution
11011012
= (1×26)+(1×25)+(0×24)+(1×23)+(1×22)+(0×21)+(1×20)
= 1×64+1×32+0×16+1×8+1×4+0×2+1×1
= 64+32+0+8+4+0+1
= 109
Therefore, 11011012 = 10910
Solution
101110011.11012
= 1×28+0×27+1×26+1×25+1×24+0×23+0×22+1×21+1×20+1×2-1+1×2-2+0×2-3+1×2-4
= 1×256+0×128+1×64+1×32+1×16+0×8+0×4+1×2+1×1+1×&frac{1}{2}+1×&frac{1}{4}+0×&frac{1}{8}+1×&frac{1}{16}
= 256+0+64+32+16+0+0+2+1+0.5+0.25+0+0.0625
= 371 + 0.8125
= 371.8125
Therefore, 101110011.11012 = 371.812510
Conversion from Decimal System to Binary System
To convert from decimal to binary, repeatedly divide the decimal number by two (2) and write down the remainder. The binary result is the remainders read from bottom to top.
Solution
2 | Dec | Remainder |
---|---|---|
2 | 109 | 1 |
2 | 54 | 0 |
2 | 27 | 1 |
2 | 13 | 1 |
2 | 6 | 0 |
2 | 3 | 1 |
2 | 1 | 1 |
0 | 1 |
Picking the remainder from bottom to top: 1101101
Therefore, 10910 = 11011012
Conversion from Octal Base System to Decimal Base System
To convert from octal to decimal, multiply each digit by an increasing power (right to left) of eight (8) and sum the result.
Solution
34568
= (3×83) + (4×82) + (5×81) + (6×80)
= (3×512) + (4×64) + (5×8) + (6×1)
= 1536 + 256 + 40 + 6
= 1838
Therefore, 34568 = 183810
Conversion from Decimal to Octal Base System
To convert from decimal to octal, repeatedly divide the decimal number by eight (8) and write down the remainder.
Solution
8 | Dec | Remainder |
---|---|---|
8 | 1838 | 6 |
8 | 229 | 5 |
8 | 28 | 4 |
8 | 3 | 3 |
0 | 3 |
Picking the remainder from bottom to top: 3456
Therefore, 183810 = 34568
Conversion from Hexadecimal base System to Decimal Base System
To convert from hexadecimal to decimal, multiply each digit by an increasing power (right to left) of sixteen (16) and sum the result.
Solution
89F16
= (8×162) + (9×161) + (F×160)
= (8×256) + (9×16) + (15×1)
= 2048 + 144 + 15
= 2207
Therefore, 89F16 = 220710
Solution
CAFE16
= (C×163) + (A×162) + (F×161) + (E×160)
= (12×4096) + (10×256) + (15×16) + (14×1)
= 49152 + 2560 + 240 + 14
= 51966
Therefore, CAFE16 = 5196610
Conversion from Decimal Base System to Hexadecimal Base System
To convert from decimal to hexadecimal, repeatedly divide the decimal number by sixteen (16) and write down the remainder.
Solution
16 | Dec | Remainder | Remainder in Hex |
---|---|---|---|
16 | 47806 | 14 | E |
16 | 2987 | 11 | B |
16 | 186 | 10 | A |
16 | 11 | 11 | B |
0 |
Picking Remainder in Hex from bottom to top: BABE
Therefore, 4780610 = BABE16
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I goggled key basic statement for jss2 I don't understand
ReplyDeleteHow may I help you
DeleteWrite a basic code of A-2
ReplyDeleteYou can can use a simple PRINT statement
DeleteE.g
CLS
REM program to display letter A -Z
PRINT "A"
PRINT "B"
complete to Z and end the program
You can also use the program below
Delete10 REM this program is written to display letters from A to Z
20 FOR I = 65 TO 90
30 PRINT CHR$(I);
40 NEXT I
50 END
Please Sir, don't really know how to calculate this = (1×26²)+(1×25²) =
ReplyDelete(1×26²)+(1×25²) = (1×26×26 )+(1×25×25 )
Delete= (676 )+(625 )
=1,301
I appreciate how it breaks down the concept of different base systems, like binary and decimal, and explains their practical applications, particularly in computing. The examples used make the content relatable and easy to understand. As someone interested in math concepts, I found the step-by-step approach to converting between bases especially helpful. This is a great resource for students looking to strengthen their understanding of number systems. I look forward to reading more educational posts like this.
ReplyDeleteI love this website
ReplyDelete