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Digital Logic Design / / / / 1 - 1 : Converting a decimal number to binary involves dividing the decimal number by 2 repeatedly
Digital Logic Design : Converting a decimal number to binary involves dividing the decimal number by repeatedly and noting down the remainders until the quotient becomes zero. The remainders, read in reverse order, give the binary equivalent of the decimal number.
Question : Can you demonstrate the conversion of the decimal number into binary?
Answer:
Divide by : Quotient Remainder
Divide by : Quotient Remainder
Divide by : Quotient Remainder
Divide by : Quotient Remainder
Divide by : Quotient Remainder
Reading the remainders from bottom to top
Getting the binary equivalent of as
: Converting a binary number to hexadecimal involves grouping the binary digits into sets of four, starting from the right side. If the leftmost group has fewer than four bits, add zeroes to make it a complete group. Then, each group is converted separately into its equivalent hexadecimal digit.
Question : Illustrate the conversion of the binary number into hexadecimal?
Answer:
group the binary digits into sets of four, starting from the right. Add leading zeroes if necessary to make complete groups of four. Then, convert each group separately into its equivalent hexadecimal digit.
Grouped the binary number as
Converting each group into its corresponding hexadecimal digit.
: Binary addition adds two binary digits, considering like base addition, but with a base of When adding binary numbers, summing two s results in with a carry of since in binary equals Adding and or two s results in the corresponding binary sum without a carry.
Question : Demonstrate the addition of the binary numbers and
Answer: Add and in binary:
: Binary subtraction subtracts one binary number from another following in base of To subtract binary numbers, borrow borrowing might be needed, and while subtracting digits, borrowing from the adjacent higherorder bit is necessary if needed.
Answer: Subtract from in binary:
: Binary multiplication multiplies binary digits following base of To multiply binary numbers, perform multiplication for each digit of one binary number with every digit of the other number, shifting as necessary, and then sum up the products to get the final result.
Question: illustrate the multiplication of the binary number by
Answer: Multiply from in binary:
multiplicand
x multiplier
Partial product: x shifted
Partial product: x
Partial product: x shifted two places left
Result: multiplied by in binary
Performing multiplication for each digit of the multiplier with the multiplicand and summing the partial products results in as the product of and in binary.
: Binary division divides one binary number dividend by another binary number divisor to obtain a quotient and a remainder.
Question : illustrate the division of the binary number by
Answer: Divide by in binary:
Quotient:
Dividend
Subtract from first division
Remainder
Subtract from second division
Remainder
Therefore, the binary division of by results in a quotient of and a remainder of
To get the s complement of a binary number, you can follow these steps:
Find the s complement of the binary number by flipping all the bits changing every to and every to
Add to the least significant bit LSB of the s complement.
For example, lets say we want to find the s complement of the binary number
The s complement of is
Adding to the LSB of gives us which is the s complement of
: s Compliment Addition adds numbers using the s complement representation to handle both positive and negative binary numbers.
To add two numbers, convert both to their s complement form, perform binary addition, and discard any overflow beyond the designated number of bits.
The result may involve discarding the carry bit to maintain the appropriate bit length.
Question : s complement addition of and in a bit syste
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