Numbers

# How decimal numbers differ from binary numbers?

91011 ###### 2011-09-12 20:19:40

Decimal numbers are in base 10 and binary numbers are in base 2. Let's take the number 135. This is equal to 100 + 30 + 5. Or 1 * 10^2 + 3 * 10^1 + 5 * 10^0. (the caret being the sign for exponent and any number greater than 0 to the exponent 0 equal 1 hence 10^0 = 1). In binary format, the base is two so the first basic number is 2^0 = 1, then 2^1 = 2, then 2^2 = 4 and so on, 8, 16, 32, 64...

to build a number like 135 in binary you may ask how many 2^8 = 256 can I fit in it? The answer is 0, then how many 2^7=128, the answer is 1. Having already allocated 128 in the number, there is only a value of 7 left to insert. That is to say that there won't be any 2^6, 2^5, 2^4, or 2^3 in it. Since 2^2 = 4 and that fits into the remaining 7 we put 1 of those. We do the same for 2^1=2 and 2^0=1 and we have the final value (0*2^8) + (1*2^7) + (0*2^6) + (0*2^5) + (0*2^4) + (0*2^3) + (1*2^2) + (1*2^1) + (1*2^0) or using only the coefficients: 010000111. Since the first zero is irrelevant, 135 in binary is 10000111!

## Related Questions A remainder is the numbers after a decimal point; sometimes used as repesenting in binary to get a binary number from a decimal number. Binary can only be 1 &amp; 0. Decimal numbers have a dot in them. Binary numbers use only 2 symbols (0 and 1) to represent different numbers, while decimal numbers use 10 symbols (0 to 9) to represent different numbers. check the below link for more. Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits). No. The set of binary numbers includes fractions which are written in binary form. For example, binary(0.1) = decimal(0.5) which is not a natural number. 25 and nothing that had a decimal point well the number 369.3125 decimal. to convert to binary it worked fine the whole number 369 by justnumber by just dividing the desired base so since i wanted binary Yes it is in "Decimal Numbers, OU " published by Professer. Samuel Damsen at the University of Wollongong.Also the link from DEW Associates in the Related Linksbelow, provides a table of Decimal, Hexadecimal, and Binary numbers from 0 to 255. In 8-bit binary, 8 ones will equal 255 (decimal). The word "understand" is a bit misleading here; computer's usually accept input as decimal, and show results as decimal numbers again. It is internally that they do most of their processing in binary, because they were so designed. And the reason they were so designed is because it is simpler to build computers that work with binary. For example, look at the multiplication table for binary numbers, and compare it to that for decimal numbers. 110.101 is already a decimal number. Unless that is intended to be two binary numbers with a decimal point between them for some reason. (decimal points are not used to represent fractional numbers in the binary system). Binary numbers belong to Binary number system. Binary System consists of only 2 digits (known as bits) 0 &amp; 1. Any no. from decimal number system can be converted to binary number system. Binary numbers are widely used in design of various digital gadgets &amp; computers. Following are some decimal no.s converted into binary numbers. Decimal number Binary number 0 0 1 1 2 10 3 11 4 100 5 101 6 110 To consider the difference between straight binary and BCD, the binary numbers need to be split up into 4 binary digits (bits) starting from the units. In 4 bits there are 16 possible values from 0000 to 1111 (0 to 15). In straight binary all of these possible combinations are used, thus: 4 bits can represent the decimal numbers 0-15 8 bits can represent the decimal numbers 0-255 12 bits can represent the decimal numbers 0-4095 16 bits can represent the decimal numbers 0-65535 etc In arithmetic, all combinations of bits are used, thus: 0000 1001 + 0001 = 0000 1010 In BCD or Binary Coded Decimal, only the representations of the decimal numbers 0-9 are used (that is 0000 to 1001 in binary), and the 4-bits (nybbles) are read as decimal digits, thus: 4 bits can represent the decimal digits 0-9 8 bits can represent the decimal digits 0-99 12 bits can represent the decimal digits 0-999 16 bits can represent the decimal digits 0-9999 In arithmetic, only the representations of decimal numbers are used, thus: 0000 1001 + 0001 = 0001 0000 When BCD is used each half of a byte is read directly as a decimal digit. BCD is obviously inefficient as storage (for large numbers) as each nybble is only holding 3/8 of the possible numbers, however, it is sometimes easier and quicker to work with decimal digits (for example when there is lots of display of counting numbers to do there is less binary to decimal conversion needing to be done).

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