Secondly - 3 bits can store 8 values Isn't that even mathematically impossible? If we were to have a switch How do 3 bits add up to 8 values?? Should be six right? Improve this question. Add a comment. Active Oldest Votes. Improve this answer. A bit can have 2 values. Neel Neel 3 3 silver badges 17 17 bronze badges.
Mohit Jain I hope this answer your question. Siddhartha Gupta Siddhartha Gupta 3 3 silver badges 11 11 bronze badges. Binary - Decimal - 0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 8 bits are grouped together to form a byte. Archie Yalakki Archie Yalakki 2 2 silver badges 10 10 bronze badges. 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? Which one of the following memory is a volatile type? Which of the following is a sequential access memory? Which of the following is NOT an external memory? This gives you 16 lines. Each line is made unique by prefixing the first half with "0" and the second half with "1". Of course, the trick can be repeated as many times as you like. Adding one more bit doubles the number of patterns. The table shows the number of patterns for 1, 2, 3 and 4 bits.
To represent an n bit signed binary number the leftmost bit, has a special significance. The difference between a signed and an unsigned number is given in the table below for an 8 bit number.
If Bit 7 is not set as in the first example the representation of signed and unsigned numbers is the same. However, when Bit 7 is set, the number is always negative. For this reason Bit 7 is sometimes called the sign bit. Signed numbers are added in the same way as unsigned numbers, the only difference is in the way they are interpreted. This is important for designers of arithmetic circuitry because it means that numbers can be added by the same circuitry regardless of whether or not they are signed.
To form a two's complement number that is negative you simply take the corresponding positive number, invert all the bits, and add 1. The example below illustrated this by forming the number negative 35 as a two's complement integer:.
So is our two's complement representation of We can check this by adding up the contributions from the individual bits. The same procedure invert and add 1 is used to convert the negative number to its positive equivalent.
If we want to know what what number is represented by , we apply the procedure again. Since represents the number 3, we know that represents the number Exercises: Convert from binary to decimal Answer Convert from binary to decimal Answer 34 Convert from decimal to binary Answer In 'C', a signed integer is usually 16 bits.
What is the largest positive number that can be represented? Consider the following examples. Let's carefully consider the last case which uses the number As a 4 bit number this is represented as.
This process is refered to as sign-extension, and can be applied whenever a number is to be represented by a larger number of bits. In the C50 Digital Signal Processor, this typically occurs when moving a number from a 16 bit register to a 32 bit register. Whether or not sign-extension is applied during such a move is determined by the sign-extension mode bit. Note that to store a 32 bit number in 16 bits you can simply truncate the upper 16 bits as long as they are all the same as the left-most bit in the resulting 16 bit number - i.
Most processors even have two separate instructions for shifting numbers to the right which, you will recall, is equivalent to dividing the number in half. The first instruction is something like LSR Logical Shift Right which simply shifts the bits to the right and usually fills a zero in as the lefmost bit.
The second instruction is something like ASR Arithmetic Shift Right , which shifts all of the bits to the right, while keeping the leftmost bit unchanged. With ASR -6 becomes The representation of unsigned binary fractions proceeds in exactly the same way as decimal fractions. Each place to the right of the decimal point represents a negative power of 2, just as for decimals they represent a negative power of Likewise, if there are m bits to the right of a decimal, the precision of the number is 2 -m versus 10 -m for decimal.
Though it is possible to represent numbers greater than one by having digits to the left of the decimal place we will restrict ourselves to numbers less than one.
These are commonly used by Digital Signal Processors. The largest number that can be represented by such a representation is -m , the smallest number is 2 -m. For a fraction with 15 bits of resolution this gives a range of approximately 0.
Note that this representationis easily extended to represent all positive numbers by having the digits to the left of the decimal point represent the integer part, and the digits to the right representing the fractional part. Exercises: Convert 0.
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