Re: Number System
From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 01/13/05
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Date: Thu, 13 Jan 2005 12:54:28 -0500
rehhman wrote:
> I read about Number system from but there are some points where my
> concepts are not clear .I will be very great full to you if you rely
> following questions to clarify my concepts:
>
> 1-What is the application of ASCII and EBCDIC (where these two code
> systems are used)?
Storing symbols.
> 2-Which coding scheme (number system) is used by computer [of course it
> is binary but what type of binary ASCII or EBCDIC]?
A coding scheme is not necessarily a number system. In particular,
ASCII and EBCDIC are coding schemes but not number systems, nor are they
types of binary. Binary is just another name for base-2.
> 3-Since ASCII and EBCDIC are 8 bit coding schemes what about a number
> 255 or greater than 255 how can we store/write these numbers in ASCII
> and EBCDIC?
This question doesn't make much sense, other than to indicate you don't
understand what they represent.
> 4-What is the application of base-8, base-16 in computer [how these
> number systems are used by computer as binary (as base-2 numbers are
> used by digital circuits)]?
Base-8 and base-16 require fewer digits to represent the same number.
> 5-In simple binary 1111=15 of decimal but 1111 of binary=11110001
> 11110101 in
> EBCDIC and 00110001 00110101 in ASCII why three different
> representation of 15 of decimal in simple binary ,ASCII and EBCDIC?
You are confusing the ASCII and EBCDIC encodings of the symbol 5 with
the mathematical base encodings of the value 5.
> 6-Why in addition of two positive numbers we preserve all bits but in
> addition of one positive and one negative number we discard bit/s if
> exceed by the max no of bits as compare to the largest digit.
> For e.g.(1) 101+110=1011 [in binary] we preserve all four bits even in
> the question the largest number consist of three bits or 5+6=11[in
> decimal]
Storage limitations. Usually, integers are stored in an one or more
bytes of storage, which corresponds to a particular number of binary
digits. Overflows are lost to avoid corrupting other areas of memory.
> e.g. (2) But 110+011=001( actual answer is 1001 but we discard right
> most bit) [in binary] [since the 2 complement of +5(101) is -5(011)]or
> 6+(-5)=1{in decimal}]
> Why in e.g.(1) we preserve all bits but in e.g. (2) we discard right
> most bit ?
>
> 7- if we just have number [not mention that its +ve or -ve ] 101 in
> base-2 how we treat this a positive number or negative number?
> Regards
It depends on your interpretation. Usually you have a fixed number of
bits/digits to work with, and you will use an appropriate encoding
scheme (1's or 2's complement) to represent negative numbers.
Googling for the various terms should help you a lot, as you seem to be
confused on a number of issues.
-- Will Twentyman email: wtwentyman at copper dot net
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