Numeric+Bases

= Numeric Bases = Numeric bases are a writing system for expressing numbers, It can be seen as the context that allows the symbols "11" to be interpreted as the [|binary] symbol for //three//, the [|decimal] symbol for //eleven//, or a symbol for other numbers in different[|bases].

Numeric Base Converter
  Numeric base converter is one that converts the numbers from one base to another base. This numeric base converter holds the conversion between bases 2 through 36.The different numeric bases used in math are as follows, >  Example: 102 >  Example: 410 >  Example: 348 >  Example: 4516 or 45H
 * <span style="background-attachment: initial; background-clip: initial; background-color: initial; url(http: //image.wistatutor.com/webimg/common/seo_spriteview.png); background-origin: initial; background-position: -134px -272px; background-repeat: no-repeat no-repeat; font-size: 12px; list-style-image: initial; list-style-position: initial; list-style-type: none; margin-bottom: 0px; margin-bottom: 8px; margin-left: 0px; margin-left: 1.4em; margin-right: 0px; margin-right: 0px; margin-top: 0.4em; margin-top: 8px; padding-bottom: 0px; padding-left: 0px; padding-left: 1.3em; padding-right: 0px; padding-top: 1px;"> Binary number having base 2.
 * <span style="background-attachment: initial; background-clip: initial; background-color: initial; url(http: //image.wistatutor.com/webimg/common/seo_spriteview.png); background-origin: initial; background-position: -134px -272px; background-repeat: no-repeat no-repeat; font-size: 12px; list-style-image: initial; list-style-position: initial; list-style-type: none; margin-bottom: 0px; margin-bottom: 8px; margin-left: 0px; margin-left: 1.4em; margin-right: 0px; margin-right: 0px; margin-top: 0.4em; margin-top: 8px; padding-bottom: 0px; padding-left: 0px; padding-left: 1.3em; padding-right: 0px; padding-top: 1px;"> Decimal number having base 10.
 * <span style="background-attachment: initial; background-clip: initial; background-color: initial; url(http: //image.wistatutor.com/webimg/common/seo_spriteview.png); background-origin: initial; background-position: -134px -272px; background-repeat: no-repeat no-repeat; font-size: 12px; list-style-image: initial; list-style-position: initial; list-style-type: none; margin-bottom: 0px; margin-bottom: 8px; margin-left: 0px; margin-left: 1.4em; margin-right: 0px; margin-right: 0px; margin-top: 0.4em; margin-top: 8px; padding-bottom: 0px; padding-left: 0px; padding-left: 1.3em; padding-right: 0px; padding-top: 1px;"> Octal number having base 8.
 * <span style="background-attachment: initial; background-clip: initial; background-color: initial; url(http: //image.wistatutor.com/webimg/common/seo_spriteview.png); background-origin: initial; background-position: -134px -272px; background-repeat: no-repeat no-repeat; font-size: 12px; list-style-image: initial; list-style-position: initial; list-style-type: none; margin-bottom: 0px; margin-bottom: 8px; margin-left: 0px; margin-left: 1.4em; margin-right: 0px; margin-right: 0px; margin-top: 0.4em; margin-top: 8px; padding-bottom: 0px; padding-left: 0px; padding-left: 1.3em; padding-right: 0px; padding-top: 1px;"> Hexadecimal number having base 16 or H.

==Example and Practice Problems: ==  **Ex 1:** Convert a decimal number 1210 into binary number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 1210 = 11002 <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Explanation:** For decimal to binary conversion we have to divide the decimal value by 2(base value of binary number) <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 12/2 - quotient is 6 and remainder is **0.** <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 6/2 - quotient is 3 and remainder is **0.** <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 3/2 - quotient is **1** and remainder is **1.** <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> So the equivalent binary value for decimal 1210 is 11002. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Ex 2:** Convert a decimal number 3110 into octal number8. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 3110 = 378 <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Explanation:** For decimal to octal conversion we have to divide the decimal value by 8(base value of octal number) <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 31/8 - quotient is **3** and remainder is **7.** <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> So the equivalent octal value for decimal 3110 is 378 <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Ex 3:** Convert a decimal number 3310 into hexadecimal number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 3310 = 21H <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Explanation:** For decimal to hexadecimal conversion we have to divide the decimal value by 16(base value of octal number) <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 33/16 - quotient is **2** and remainder is **1.** <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> So the equivalent hexadecimal value for decimal 3310 is 21H. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Ex 4:** Convert a octal number 128 into hexadecimal number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 12 8= AH <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Explanation:** For octal to hexadecimal conversion first we have to convert octal to decimal and then decimal to hexadecimal. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> Octal number 128 can be converted into decimal number as follows. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 12 8= (1 X 81)+(2 X 80) <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> = 8 +2 <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> = 10. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> 10 can be denoted as **A** in hexadecimal whereas **B**=11,**C**=12,**D**=13,**E**=14,**F**=15. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Practice problems:** <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Q 1:** Convert a decimal number 1510 into binary number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Answer :** 1510= 11112. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Q 2:** Convert a decimal number 1910 into octal number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 1910= 238. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Q 3:** Convert a decimal number 5610 into hexadecimal number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 5610 = 38H. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Q 4:** Convert a octal number 458 into hexadecimal number. <span style="font-size: 12px; margin-bottom: 2px; margin-left: 0px; margin-right: 0px; margin-top: 2px; padding-bottom: 5px; padding-top: 5px;"> **Sol :** 458= 25H.