DIGITAL NUMBER SYSTEM

DIGITAL NUMBER SYSTEMPREPARED BY: Ms. Ivy RazonalesAset of values used to represent different quantities is known asNumber System".

For example, a number system can be used to represent the number of students in a class or number of viewers watching a certain TV program etc. The digital computer represents all kinds of data and information in binary numbers. It includes audio, graphics, video, text and numbers

1DECIMAL NUMBER SYSTEMThe number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represents ones, tens, hundreds, thousands and so on.DECIMAL NUMBER SYSTEMExample:12344 - ONES3 - TENS2 HUNDREDS1 - THOUSANDS=(1x103)+ (2x102)+ (3x101)+ (4xl00)=(1x1000)+ (2x100)+ (3x10)+ (4xl)=1000 + 200 + 30 + 4=1234BASE 10489722 - ONES7 - TENS9 HUNDREDS8 THOUSANDS4 TEN THOUSANDS=(4x104)+ (8x103)+ (9x102)+ (7x101)+ (2xl00)=(4x 10000)+ (8x1000)+ (9x100)+ (7x10)+ (2xl)=40000 + 8000 + 900 + 70 + 2=48972DIGITAL NUMBER SYSTEMAs a professional, you should understand the following number systems which are frequently used in computers.

NUMBER SYSTEMBASEDIGITS USEDBINARY20 AND 1OCTAL80 TO 7HEXA DECIMAL160 TO 9 AND LETTERS: A TO FThe decimal number system is used in general. However, the computers use binary number system. The octal and hexadecimal number systems are used in the computer.4BINARY NUMBER SYSTEMCharacteristics:Uses two digits, 0 and 1.Also called base 2 number systemFirst position in a binary number represents a 0 power of the base (2). Example 20Last position in a binary number represents a x power of the base (2). Example 2x

BINARY NUMBER SYSTEMExample:101012=((1x24)+ (0x23) +(1x22) +(0x21) +(1x20)) 10=((1x16)+ (0x8) + (1x4) + (0x2) +(1x1)) 10=( 16 + 0 + 4 + 0 + 1 ) 10= (21) 10 or 2110 1010111012=((1x28) + (0x27) + (1x26)+ (0x25)+ (1x24)+ (1x23) +(1x22) +(0x21) +(1x20)) 10=((1x256)+ (0x128)+ (1x64)+ (0x32)+ (1x16)+ (1x8) + (1x4) + (0x2) +(1x1)) 10=( 256 + 0 + 64 + 0 + 16 + 8 + 4 + 0 + 1 ) 10= (349) 10 or 34910 OCTAL NUMBER SYSTEMCharacteristics:Uses eight digits, 0,1,2,3,4,5,6,7Also called base 8 number systemFirst position in a octal number represents a 0 power of the base (8). Example 80Last position in a octal number represents a x power of the base (8). Example 8x

OCTAL NUMBER SYSTEMExample:125708=((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10=(4096 + 1024 + 320 + 56 + 0)10=54961016345218=((1 x 86) + (6 x 85) +(3 x 84) + (4 x 83) + (5 x 82) + (2 x 81) + (1 x 80))10=(262144 + 196608 + 12288 + 2048 + 320 + 16 + 1)10=47342510HEXA DECIMAL NUMBER SYSTEMCharacteristics:Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.Letters represents numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15.Also called base 16 number systemFirst position in a hexadecimal number represents a 0 power of the base (16). Example 160Last position in a hexadecimal number represents a x power of the base (16). Example 16x

HEXA DECIMAL NUMBER SYSTEMExample: 19FDE16=((1 x 164) + (9 x 163) + (F x 162) + (D x 161) + (E x 160))10= ((1 x 164) + (9 x 163) + (15 x 162) + (13 x 161) + (14 x 160))10=(65536+ 36864 + 3840 + 208 + 14)10=10646210 28ABC16=((2 x 164) + (8 x 163) + (Ax 162) + (B x 161) + (C x 160))10=((2 x 164) + (8 x 163) + (10 x 162) + (11 x 161) + (12 x 160))10=(131072+ 32768 + 2560+ 176+ 12)10=16658810QUIZ #1QUIZ#1CHANGE THE FOLLOWING INTO DECIMAL (BASE OF 2)

10110011121111100011210101011002542891008874927120087632129982A4B8C16D87E3F16FE761016