Computers do much of their processing in binary. Hexadecimal is used as a kind of shortcut (easier to read for humans): each hexadecimal digit represents four binary digits.
Almost exactly like the decimal system, but the base is the number 2, instead of the number 10. This refers to the place-value system: in decimal, each digit has a place-value that is 10 times as much as the digit on the right; in binary, the factor is 2. It is helpful if you understand the place-value system in decimal first.
1Set up the problem. For this example, let's convert the decimal number 15610 to binary. Write the decimal number as the dividend inside an upside-down "long division" symbol. Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol.This method is much easier to understand when visualized on paper, and is much easier for beginners, as it relies only on division by two.To avoid confusion before and after conversion, write the number of the base system that you are working with as a subscript of each number. In this case, the decimal number will have a subscript of 10 and the binary equivalent will have a subscript of 2.2 Divide. Write the integer answer (quotient) under the long division symbol, and write the remainder (0 or 1) to the right of the dividend.[2]Since we are dividing by 2, when the dividend is even the binary remainder will be 0, and when the dividend is odd the binary remainder will be 1.3 Continue to divide until you reach 0. Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.4Write out the new, binary number. Starting with the bottom remainder, read the sequence of remainders upwards to the top. For this example, you should have 10011100. This is the binary equivalent of the decimal number 156. Or, written with base subscripts: 15610 = 100111002This method can be modified to convert from decimal to any base. The divisor is 2 because the desired destination is base 2 (binary). If the desired destination is a different base, replace the 2 in the method with the desired base. For example, if the desired destination is base 9, replace the 2 with 9. The final result will then be in the desired base.
The number 100010000001000000 is 100,010,000,001,000,000 which is (short scale, US) 100 quadrillion, 10 trillion, and 1 million. Decimally, this is 1.00010000001 x 1017 or [ 1 x 1017 + 1 x 1013 + 1 x 106 ] If the number is a binary number it is equivalent to 139,328 in decimal
A decimal is a form of representing a number. It has no area at all.
Because it's much, much easier to design electronic two-way switches that electronic ten-way switches. A two-way switch leads to binary.
Computers do much of their processing in binary. Hexadecimal is used as a kind of shortcut (easier to read for humans): each hexadecimal digit represents four binary digits.
Binary numbers all consist of combinations of the two digits '0' and '1'. These are some examples of binary numbers: 11010101111101111000000 10101000 00001100 01011101Engineers and mathematicans sometimes call the binary numbering system a base-two system because binary numbers only contain two digits. By comparison, our normal decimal number system is a base-ten system. Hexadecimal numbers (discussed later) are a base-sixteen system. All binary numbers have equivalent decimal representations and vice versa. Our handy Binary-Decimal Number Converter performs these calculations automatically for you. To convert binary and decimal numbers manually, you must apply the mathematical concept of positional values. The positional value concept is simple: With both binary and decimal numbers, the actual value of each digit depends on its position (how "far to the left") within the number. For example, in the decimal number 124, the digit '4' represents the value "four," but the digit '2' represents the value "twenty," not "two." The '2' represents a larger value than the '4' in this case because it lies further to the left in the number. Likewise in the binary number 1111011, the rightmost '1' represents the value "one," but the leftmost '1' represents a much higher value ("sixty-four" in this case). In mathematics, the base of the numbering system determines how much to value digits by position. For base-ten decimal numbers, multiply each digit on the left by a progressive factor of 10 to calculate its value. For base-two binary numbers, multiply each digit on the left by a progressive factor of 2. Calculations always work from right to left. In the above example, the decimal number 123 works out to: 3 + (10 * 2) + (10*10 * 1) = 123and the binary number 1111011 converts to decimal as: 1 + (2 * 1) + (2*2 * 0) + (4*2 * 1) + (8*2 * 1)+ (16*2 * 1) + (32*2 * 1) = 123Therefore, the binary number 1111011 is equal to the decimal number 123. To convert numbers in the opposite direction, from decimal to binary, requires successive division rather than progressive multiplication. Our Binary-Decimal Number Converter also performs these calculations automatically for you. To manually convert from a decimal to a binary number, start with the decimal number and begin dividing by the binary number base (base "two"). For each step the division results in a remainder of 1, use '1' in that position of the binary number. When the division results in a remainder of 0 instead, use '0' in that position. Stop when the division results in a value of 0. The resulting binary numbers are ordered from right to left. For example, the decimal number 109 converts to binary as follows: 109 / 2 = 54 remainder 154 / 2 = 27 remainder 027 / 2 = 13 remainder 113 / 2 = 6 remainder 16 / 2 = 3 remainder 03 / 2 = 1 remainder 11 / 2 = 0 remainder 1Therefore the decimal number 109 equals the binary number 1101101. (Credit to About.com) Binary numbers all consist of combinations of the two digits '0' and '1'. These are some examples of binary numbers: 11010101111101111000000 10101000 00001100 01011101Engineers and mathematicans sometimes call the binary numbering system a base-two system because binary numbers only contain two digits. By comparison, our normal decimal number system is a base-ten system. Hexadecimal numbers (discussed later) are a base-sixteen system. All binary numbers have equivalent decimal representations and vice versa. Our handy Binary-Decimal Number Converter performs these calculations automatically for you. To convert binary and decimal numbers manually, you must apply the mathematical concept of positional values. The positional value concept is simple: With both binary and decimal numbers, the actual value of each digit depends on its position (how "far to the left") within the number. For example, in the decimal number 124, the digit '4' represents the value "four," but the digit '2' represents the value "twenty," not "two." The '2' represents a larger value than the '4' in this case because it lies further to the left in the number. Likewise in the binary number 1111011, the rightmost '1' represents the value "one," but the leftmost '1' represents a much higher value ("sixty-four" in this case). In mathematics, the base of the numbering system determines how much to value digits by position. For base-ten decimal numbers, multiply each digit on the left by a progressive factor of 10 to calculate its value. For base-two binary numbers, multiply each digit on the left by a progressive factor of 2. Calculations always work from right to left. In the above example, the decimal number 123 works out to: 3 + (10 * 2) + (10*10 * 1) = 123and the binary number 1111011 converts to decimal as: 1 + (2 * 1) + (2*2 * 0) + (4*2 * 1) + (8*2 * 1)+ (16*2 * 1) + (32*2 * 1) = 123Therefore, the binary number 1111011 is equal to the decimal number 123. To convert numbers in the opposite direction, from decimal to binary, requires successive division rather than progressive multiplication. Our Binary-Decimal Number Converter also performs these calculations automatically for you. To manually convert from a decimal to a binary number, start with the decimal number and begin dividing by the binary number base (base "two"). For each step the division results in a remainder of 1, use '1' in that position of the binary number. When the division results in a remainder of 0 instead, use '0' in that position. Stop when the division results in a value of 0. The resulting binary numbers are ordered from right to left. For example, the decimal number 109 converts to binary as follows: 109 / 2 = 54 remainder 154 / 2 = 27 remainder 027 / 2 = 13 remainder 113 / 2 = 6 remainder 16 / 2 = 3 remainder 03 / 2 = 1 remainder 11 / 2 = 0 remainder 1Therefore the decimal number 109 equals the binary number 1101101. (Credit to About.com)
Almost exactly like the decimal system, but the base is the number 2, instead of the number 10. This refers to the place-value system: in decimal, each digit has a place-value that is 10 times as much as the digit on the right; in binary, the factor is 2. It is helpful if you understand the place-value system in decimal first.
1Set up the problem. For this example, let's convert the decimal number 15610 to binary. Write the decimal number as the dividend inside an upside-down "long division" symbol. Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol.This method is much easier to understand when visualized on paper, and is much easier for beginners, as it relies only on division by two.To avoid confusion before and after conversion, write the number of the base system that you are working with as a subscript of each number. In this case, the decimal number will have a subscript of 10 and the binary equivalent will have a subscript of 2.2 Divide. Write the integer answer (quotient) under the long division symbol, and write the remainder (0 or 1) to the right of the dividend.[2]Since we are dividing by 2, when the dividend is even the binary remainder will be 0, and when the dividend is odd the binary remainder will be 1.3 Continue to divide until you reach 0. Continue downwards, dividing each new quotient by two and writing the remainders to the right of each dividend. Stop when the quotient is 0.4Write out the new, binary number. Starting with the bottom remainder, read the sequence of remainders upwards to the top. For this example, you should have 10011100. This is the binary equivalent of the decimal number 156. Or, written with base subscripts: 15610 = 100111002This method can be modified to convert from decimal to any base. The divisor is 2 because the desired destination is base 2 (binary). If the desired destination is a different base, replace the 2 in the method with the desired base. For example, if the desired destination is base 9, replace the 2 with 9. The final result will then be in the desired base.
It's quite easy to convert binary into hexadecimal (hex) by grouping each 4 binary digits (bits) into a single binary hex digit: 0A 64 07 15 From there it's easier to convert into decimal in the head: 10 100 7 21 If you will be doing much in the way of programming computers, or working with TCP/IP networking, it is definitely a good idea to spend some time familiarising yourself with hexadecimal and converting between hex, binary and decimal. For reference, converting from binary to hex is done like this: 0000 = 0 0001 = 1 0010 = 2 0011 = 3 0100 = 4 0101 = 5 0110 = 6 0111 = 7 1000 = 8 1001 = 9 1010 = A 1011 = B 1100 = C 1101 = D 1110 = E 1111 = F
The number 100010000001000000 is 100,010,000,001,000,000 which is (short scale, US) 100 quadrillion, 10 trillion, and 1 million. Decimally, this is 1.00010000001 x 1017 or [ 1 x 1017 + 1 x 1013 + 1 x 106 ] If the number is a binary number it is equivalent to 139,328 in decimal
It tells you exactly how much you have if that amount is not a whole number.
A decimal is a form of representing a number. It has no area at all.
A synchronous or asynchronous stream of signal consisting only of zero(no voltage) and one(position voltage) is called binary data stream. They may be bytestream, wordstream and so on. Sending unique binary pulses periodically create a binary digital signal. For example, you want to pass the number 346F5A through binary digital signal it will be 001101000110111101011010 Break it 0011-0100-0110-1111-0101-1010 you will find the binary equivalents of each digit. This example is very simple. Usually complex form of data are sent to and fro through data lines, be it the SATA cable of your hard drive, the USB port or the Internet.
The addition and multiplication table is much simpler. Also, on a computer it is easier to distinguish two different states than ten different states. For these reasons, modern computers do most of their calculations internally in binary.
415 is a perfectly valid decimal number. So the answer is 415 inches.