8 bits how many values

If this bit is set, the number is negative, otherwise the number is positive. The largest positive number that can be represented is still -m but the largest negative number is The resolution is still -m. There is a terminology for naming the resolution of signed fractions. If there are m bits to the right of the decimal point, the number is said to be in Q m format. For a 16 bit number 15 bits to the right of the decimal point this results in Q15 notation. Exercises: Convert 1. Signed binary fractions are easily extended to include all numbers by representing the number to the left of the decimal point as a 2's complement integer, and the number to the right of the decimal point as a positive fraction.

Note, that as with two's complement integers, the leftmost digit can be repeated any number of times without affecting the value of the number. Another way to convert Q m numbers to decimal is to represent the binary number as a signed integer, and to divide by 2 m. To convert a decimal number to Q m , multiply the number by 2 m and take the rightmost m digits. Note, this simply truncates the number; it is more elegant, and accurate, but slightly more complicated, to round the number.

Comments or Questions? Representation of Numbers. Decimal Hexadecimal Binary 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 A 11 B 12 C 13 D 14 E 15 F Binary Unsigned Signed 35 35 -1 Decimal 4 bit 8 bit 3 -3 7 -5 Convert 1. Convert 0. The answer is This is represented in binary as , so the Q7 representation is 0.

This agrees with the result of the previous exercise Positive Binary Fractions. Convert The Q7 representation is 1. This agrees with the result of the previous exercise Signed Binary Fractions.

This section is not complete. In 'C', an unsigned integer is usually 16 bits. Convert 37 to binary, shift it left by one and convert back to decimal. What is the result. Answer 7D0. Answer A7B. If you shift a hexadecimal number to the left by one digit, how many times larger is the resulting number?

In 'C', a signed integer is usually 16 bits. What is the largest negative number that can be represented? Answer 0. Answer 1. The Lilliputians considered the big endians as inferiors. The big endians fought a long and senseless war with the Lilliputians who insisted it was only proper to break an egg on the little end. A boolean number is has two states. The two values could represent the logical true or false.

The positive logic representation defines true as a 1 or high, and false as a 0 or low. If you were controlling a motor, light, heater or air conditioner the boolean could mean on or off. In communication systems, we represent the information as a sequence of booleans: mark or space. For black or white graphic displays we use booleans to specify the state of each pixel. The most efficient storage of booleans on a computer is to map each boolean into one memory bit.

In this way, we could pack 8 booleans into each byte. If we have just one boolean to store in memory, out of convenience we allocate an entire byte or word for it.

Most C compilers including Keil uVision define:. Decimal numbers are written as a sequence of decimal digits 0 through 9. The number may be preceded by a plus or minus sign or followed by a L or U. Lower case l or u could also be used.

The minus sign gives the number a negative value, otherwise it is positive. The plus sign is optional for positive values. Unsigned bit numbers between and should be followed by U. You can place a L at the end of the number to signify it to be a bit signed number. The range of a decimal number depends on the data type as shown in the following table. On the Keil uVision compiler, the char data type may be signed or unsigned depending on a compiler option.

Because the ARM Cortex microcomputers are most efficient for 32 bit-data and not bit data , the unsigned int and int data types are 32 bits. On the other hand, on a 9Sbased machine, the unsigned int and int data types are 16 bits. In order to make your software more compatible with other machines, it is preferable to use the short type when needing bit data and the long type for bit data. Since the Cortex M microcomputers do not have direct support of bit numbers, the use of long long data types should be minimized.

On the other hand, a careful observation of the code generated yields the fact that these compilers are more efficient with bit numbers than with 8-bit or bit numbers. The manner in which decimal literals are treated depends on the context. If a sequence of digits begins with a leading 0 zero it is interpreted as an octal value. There are only eight octal digits, 0 through 7. As with decimal numbers, octal numbers are converted to their binary equivalent in 8-bit or bit words.

The range of an octal number depends on the data type as shown in the following table. Notice that the octal values 0 through 07 are equivalent to the decimal values 0 through 7. One of the advantages of this format is that it is very easy to convert back and forth between octal and binary.

The hexadecimal number system uses base 16 as opposed to our regular decimal number system that uses base Like the octal format, the hexadecimal format is also a convenient mechanism for us humans to represent binary information, because it is extremely simple for us to convert back and forth between binary and hexadecimal. A nibble is defined as 4 binary bits. Each value of the 4-bit nibble is mapped into a unique hex digit. Computer programming environments use a wide variety of symbolic notations to specify the numbers in various bases.

The following table illustrates various formats for numbers. If a sequence of digits begins with 0x or 0X then it is taken as a hexadecimal value. In this case the word digits refers to hexadecimal digits 0 through F. As with decimal numbers, hexadecimal numbers are converted to their binary equivalent in 8-bit bytes orbit words. Bytes in larger numbers can also be called least significant and most significant. The largest number you can represent with 8 bits is , or in decimal notation.

Get Started for Free Download App. More Memory Questions Q1. Which of the following Storage device can store maximum amount of data? Another term for main memory is. Which is not a type of secondary memory?

Which one of the following is a ROM type? If the switch is on, then the bit has the value one. A bit can only represent two different values, zero or one. To represent larger pieces of information, bits are strung together in sequences of 8 called bytes. A byte can represent any value from through , for a total of different possible values. Each digit in a byte can be thought of as representing an individual switch that is either off zero or on one. Modern computers rely on transistors, which pack millions of tiny switches into a chip smaller than your thumb, but information is still represented in essentially the same way: as a series of ones and zeros.

By using binary, computers can represent information simply and efficiently using a system that is very effectively modeled in digital circuitry.