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Describe the range of numbers that can be represented by a 16 bit number using two complement?
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∙ 10y ago
A signed 16 bit number can represent the decimal numbers -32768 to 32767.
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∙ 10y ago
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What are the advantages of 2's complement?
In sign magnitude, zero is represented in 2 ways so we have one less number that can be represented. Double representation can also cause problems when comparing numbers; numbers may be the same but look different.Addition and subtraction are very easy in 2's complement. To compute 6-2, we just add 6 to -2 using normal addition dropping the leftmost carry bit if there is any carry:01102 = 611102 = -2---------------01002 = 4
What is the difference between the twos complement representation of a number and the twos complement of a number?
Let's consider any number, for example a byte of data represented as eight bits. The values that this byte can have are 00000000 through 11111111. The easiest way to find the one's complement is to change the zeros to one and the ones to zeros. The limits shown above can be represented as 00 through FF in hexadecimal. Let's consider a number AF which is within this boundary. The easiest way to find the one's complement when numbers are represented in hexadecimal form is to subtract the number from (in this case) FF. You will have more F's depending on the length of the number you want to find the one's complement for. If the number consists of three hex digits then you subtract from FFF, if four then from FFFF and so on. Thus with our example of AF, its one's complement would be FF AF --- 50 --- If you add 1 to this result you will get the two's complement of the number AF. Hence the two's complement of AF is (50 + 1) = 51 in hex. Observe that the process of finding one's complement or two's complement of a number are reversible and the original number is obtained. Thus the one's complement of the one's complement of a number gives the original number. The two's complement of the two's complement of a number gives the original number. Lets consider the hex number FF. Its one's complement is 00 and the two's complement is 01. So far we have talked about two's complement of a number (and in the process the one's complement as well). It is not possible to explain two's complement representation without understanding hardware implementation on a computing device, namely, a computer. Let's consider a byte machine where you can operate only on single bytes. Thus you can add two bytes, subtract a byte from another and so on. If two's complement representation of numbers is not implemented on a machine, then the byte can hold values hex 00 through hex FF which would be 0 through 255 in decimal. If 1 is added to a byte containing FF on this machine, the contents of the byte will change to 0 and the overflow bit in the computer will be set to TRUE. If however, two's complement representation of numbers is implemented on a machine the MSB (most significant bit) in the byte is the sign bit. If it is set then the number is negative and if it is not set then the number is positive. Since one bit of the 8 bits in our byte machine is taken up to represent the sign, only the remaining 7 bits can hold the magnitude of the number. The range of positive number in such a machine is hex 00 through hex 7F which is 0 through 127. If you add 1 to 7F then the contents of the byte would be hex 80. Notice that this is a negative number because the MSB is set. But how negative is this number. Since the machine implements two's complement representation of number on this machine, subtract (hex 80) from hex FF and add 1 to get hex 80 which equals 128. So the byte machine which implements two's complement can represent values from -128 through +127. In general if a machine implements 16, 32, or 64 bit architecture, the numbers that they can hold if they implement two's complement are between -(2*n) through and including +(2*n - 1) where n is 16, 32, or 64. I hope you have a better understanding of the difference between two's complement of a number and its representation (meaning implementation) on a computer.
What hexadecimal numbers are represented by decimal number 28?
28 = 11100
Which is the symbol used to write a whole number?
The set of whole numbers is represented by Z.
The twos complement of 11001101 is?
00110011 is the 2's complement for this unsigned number and 10110011 if this is a signed number
Describe the range of numbers that can be represented by a 8 bit number using two complement?
-128 to 127
How do you write an irrational number in algebra?
There is no representation for irrational numbers: they are represented as real numbers that are not rational. The set of real numbers is R and set of rational numbers is Q so that the set of irrational numbers is the complement if Q in R.
Difference in 1's and 2's Complement?
1's Complement, has two different codes for the number 0 (+0 & -0), negative numbers are the simple binary complement of positive numbers, is symmetrical (same number of negative and positive numbers can be represented), adder/subtractor must implement wraparound carry from MSB to LSB to get correct answer2's Complement, has only one code for the number 0 (+0), negative numbers are 1 greater than the simple binary complement of positive numbers, is asymmetrical (one extra negative number than positive numbers), adder/subtractor is identical to a simple unsigned binary adder/subtractor without any special carry circuits needed
What are 1's and 2's complement numbers explain?
1's complement numbers are those numbers which are obtain after converting 1 to 0 and 0 to 1. for e.g. 110010 1's complement of this number is:001101 2's complement is obtain by adding 1 in 1's complement of number. for e.g. 2's complement of above number:001101 + 1 --------------- 001110
Explain the methods which are available to store negative numbers and how are they used. Which method is mainly used today and why?
signed magnitude, one bit indicates the sign of the number and the other bits indicate the positive magnitude of the number (this system has two representations for zero: +0 and -0)one's complement, positive numbers are represented as their positive magnitude and negative numbers are represented as the complement of their positive magnitude (this system has two representations for zero: +0 and -0)two's complement, positive numbers are represented as their positive magnitude and negative numbers are represented as the complement of their positive magnitude plus one (this system is asymmetric about zero, with one more negative value than positive)offset binary, numbers are represented as the positive sum of their actual value and an offset (this system is asymmetric about zero, typically with one more negative value than positive)Most modern systems use two's complement for fixed point numbers (because the arithmetic circuitry is simpler than the others) and a combination of signed magnitude and offset binary for floating point numbers (because this format allows the same instructions for comparing fixed point numbers to also be used to compare floating point numbers, reducing the number of different instructions and the circuitry to implement them),
What is a real number represented by?
The set of real numbers is represented by a fancy script "R". However, real numbers are just represented by a number (be it integer, rational, irrational, or otherwise). The key here is that it is not a complex number (number containing the imaginary number "i").
How many decimal numbers can be represented by 4-bits?
There are 16 decimal numbers that can be represented by 4-bits.
Can irrational numbers cannot be represented by points on the real number line?
These number can also be represented on real line.
What is the 8-bit sign-and-magnitude representation of the decimal number -2?
10
Do irrational numbers repeat?
No. Irrational numbers are those that cannot be represented as a fractions. Any number which repeats could be represented as a fraction.
The largest number that can be represented by one byte is?
The biggest number that can be represented in one byte is 11111111. Binary numbers have the ability to added together in a fashion similar to decimal numbers.
What are the advantages of 2's complement?
In sign magnitude, zero is represented in 2 ways so we have one less number that can be represented. Double representation can also cause problems when comparing numbers; numbers may be the same but look different.Addition and subtraction are very easy in 2's complement. To compute 6-2, we just add 6 to -2 using normal addition dropping the leftmost carry bit if there is any carry:01102 = 611102 = -2---------------01002 = 4
