0
To convert any number in any base to another base, simply iteratively divide by the second base, using the rules of arithmetic for the first base, recording the remainders in reverse order, until the quotient is zero. For example, answering the question of how to convert 9310 to 10111012...
93 divided by 2 is 46 remainder 1
46 divided by 2 is 23 remainder 0
23 divided by 2 is 11 remainder 1
11 divided by 2 is 5 remainder 1
5 divided by 2 is 2 remainder 1
2 divided by 2 is 1 remainder 0
1 divided by 2 is 0 remainder 1
The answer, reading the remainders from bottom to top, is 10111012.
This was not a good example, because the answer is palindromic, and can be read the same way forwards and backwards. Here is another example, converting 3710 into 1001012.
37 divided by 2 is 18 remainder 1
18 divided by 2 is 9 remainder 0
9 divided by 2 is 4 remainder 1
4 divided by 2 is 2 remainder 0
2 divided by 2 is 1 remainder 0
1 divided by 2 is 0 remainder 1
The answer is 1001012.
Wiki User
∙ 12y ago
Wiki User
∙ 11y agoTo convert any decimal value to binary, divide by two repeatedly, and if there is a remainder, mark it as a binary one value, otherwise mark it as a binary zero value. When you are done with the division, you reverse the order of the bits. So, you would do this:
97/2 = 46 r 1
46/2 = 23 r 0
23/2 = 11 r 1
11/2 = 5 r 1
5/2 = 2 r 1
2/2 = 1 r 0
1/2 = 0 r 1
When you read the remainders from bottom to top, you get 0101 1101 (64+16+8+4+1). There are always a multiple of 8 bits to a byte, so the left-most spot, which we didn't have a number for, was filled with a 0.
Add your answer:
Earn +20 pts
What is number system what are various number system explain with a suitable example?
A number system is simply a way to record numbers. Humans have used a variety of numbering systems over the years, but the decimal system is by far the most prevalent today. This system uses the ten Arabic symbols, 0123456789, to represent the digits from zero to nine, and is known as base 10 for this reason. Digits are aligned on columns, with units on the right, 10s to their left, and 100's to their left, and so on. Each column is therefore 10 times the value of the column to its right. In other words, each column is an increasing power of 10, beginning with 10^0 on the right, then 10^1 and so on. You are undoubtedly familiar with base 10, however the above is relevant when discussing other number systems as the same principals apply. Computers use base 2 (binary), which is the lowest base of all. It uses the 2 Arabic digits, 0 and 1. Since it is base 2, the columns represent powers of 2. So the rightmost column represents 2^0, then 2^1, 2^2, 2^3, and so on the further left we go. So the number 4 in decimal would be represented by 100 in base 2. That is, 1 * (2^2), which is 4 (all other columns are zero, so they evaluate to zero). Computer programmers use base 16 (hexadecimal). This is because binary numbers, despite their apparent simplicity, are incredibly difficult for humans to work with. One digit out of place could be disastrous. Converting them to decimal is clearly an option, but hexadecimal is a lot simpler to work with because base 2 and base 16 are interchangeable and align with each other more closely than decimal. Four binary digits gives us 16 possible combinations. 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110 and 1111 (decimal zero to decimal 15, respectively). With only 16 combinations to consider, each of these can be represented by a single hexadecimal symbol. There are only 10 Arabic symbols for numbers, so we must use 6 additional symbols for the numbers 10 to 15. By convention we use the letters a through f. Thus each of the binary combinations above can be represented by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e and f, respectively. Binary digits (bits) are usually combined into groups of 8 bits, known as bytes. 8 is a multiple of 4, so we need 2 hexadecimal digits to represent a full byte. To do this we simply divide the byte into two half bytes (known as nybbles), then convert each nybble to its hexadecimal form. Thus the byte 01101101 is represented as nybbles 0110 and 1101, which is 5d in hexadecimal (often denoted as 0x5d). This equates to (5 * (16^1)) + (13 * (16^0)), which is 93 decimal. So 01101101 is binary for 93 decimal, or 0x5d hexadecimal. Regardless of the length of a sequence of bits, breaking them into groups of 4 allows them to be translated directly into hexadecimal. So a 32-bit number requires 8 hexadecimal digits. Reading and writing 8 digits is clearly a lot simpler than deciphering 32 bits of 1s and 0s, and because binary and hexadecimal have a consistent alignment (4 bits equals 1 hex digit), they are much easier to deal with than decimal which has a more variable alignment with binary (4 bits could be 1 or 2 decimal digits). Other bases that are in common use today include base 60, which is the basis for our clocks. 60 seconds is 1 minute and 60 minutes is 1 hour. Then we switch to base 12 for the hours (or base 24 if using a 24-hour clock). You may ask why we never "decimalised" our time-keeping (dividing the day into 10 or 20 longer hours, each with 100 minutes, each with 100 seconds, for instance). The main reason is that 60 is evenly divisible by 2, 3, 4, 5 and 6, whereas 100 is evenly divisible by just 2, 4 and 5, and a 12-hour period (which is also division of 60) is evenly divisible by 2, 3, 4 and 6 whereas 10 is evenly divisible by just 2 and 5. Inches and feet are also base 12. So while we are quite familiar with base 10, we actually use other bases without realising it. Of course we don't symbolise numbers greater than 9 with letters like we do in hexadecimal, but the principal is the same.
Which number is less than the product 35 and 2.58 A 90.03 B 90.3 C 90.33 or D 93?
The answer is A 90.03
What is 93 plus -22?
93 + (-22) = 71
Decimal numbers into their equivalent binary numbers?
#include #includevoid main(){int a[20],b,c,d,i=0;printf("Enter a decimal no. to convert it into binary no.");scanf("%d",&b);c=b;while(b>0){d[i]=b%2;i++;b=b/2;}i--;printf("\nBinary equivalent of decimal no. %d is ",c);while(i>=0){printf("%d",d[i]);i--;}getch();}
What is 96 plus 93 plus 98?
96 + 93 + 98 = 287
What is the decimal form of 93?
A decimal number is simply a way of representing a number in such a way that the place value of each digit is ten times that of the digit to its right. A decimal representation does not require a decimal point. So the required decimal representation is 93, exactly as in the question.
What decimal is equivalent to 93 percent?
93% is equivalent to 93/100 or 0.93 in decimal form.
How do you convert the recurring decimal 0.349 when only 3 and 9 recur?
If I understand your question correctly, you are asking to convert 0.34939393939393... to a fraction.0.34939393...= 0.34 + 0.0093939393... • separate the recurring and non-recurring parts= 34/100 + (93/99 ÷ 100) • convert both parts to fractions= 34/100 + 93/9900= (34*99)/9900 + 93/9900 • convert fractions to common denominator= (3366 + 93)/9900= 3459/9900 • divide by common factor of 3= 1153/3300, which is your final answer in simplified formIf that's not the decimal you were trying to convert, then follow a similar procedure for the number you need.
What is 93 over 1000 converted to a decimal?
93/1000 as a decimal is 0.093
What is the decimal for 93 percent?
93% = 0.93
How do you convert 93.08 into a mixed number?
It is: 93 and 2/25 reduced to its simplest form
How much is 92.5 when you convert it?
Rounded to the nearest whole number 92.5 becomes 93
What is 22.38 -93?
115.38
What is 93¾ into a decimal?
93.75
What is 93 over 100 as a decimal?
93/100 = 0.93
What is 93 rounded to the nearest hundredth?
93.00
What is 93 over 125 as a decimal?
93 over 125 is 0.744.
