How do you convert fractional binary numbers in decimal?

Answer 1

The basic way of doing it with pencil and paper.

# Write down "0." (i.e. "zero point") # Start with n=-1 and your number x # If 2^n > x, then decrement n, and write down a "0". Keep repeating until 2^n < x. # Let x = x - 2^n, and decrement n. # If x is 0, you're done. Otherwise, return to step 3. Here's an infinite example, converting 0.7 to a decimal

# At step 1. We have written down "0." # At step 2. n=-1, x=0.7. # At step 3. 2^-1 = 0.5, which is less than x (now 0.7)

# At step 4. Let x = 0.7 - 0.5 = 0.2. Decrement n to -2. We have written down "0.1" # At step 5. x is not 0, so we return to step 3. # At step 3. 2^-2 = 0.25, which is greater than x (now 0.2). Decrement n to -3. We have written down "0.10"

# At step 3. 2^-3 = 0.125, which is less than x (now 0.2). # At step 4. Let x = 0.2 - 0.125 = 0.075. Decrement n to -4. We have written down "0.101". # At step 5. x is not 0, so we return to step 3. # At step 3. 2^-4 = 0.0625, which is less than x (now 0.075). # At step 4. Let x = 0.075 - 0.0625 = 0.0125. Decrement n to -5. We have written down "0.1011". # At step 5. x is not 0, so we return to step 3. # At step 3. 2^-5 = 0.03125, which is greater than x (now 0.0125). Decrement n to -6. We have written down "0.10110". # At step 3. 2^-6 = 0.015625, which is still greater than x. Decrement n to -7. We have written down "0.101100". # At step 3. 2^-7 = 0.0078125, which is less than x (now 0.0125). # At step 4. Let x = 0.0125 - 0.0078125 = 0.0046875. Decrement n to -8. We have written down "0.1011001". # At step 5. x is not 0, so we return to step 3. # Et cetera ad nauseum

Answer 2

The simplest way to convert a fraction to a decimal is to get the denominator to equal 100. To do this, simply divide 100 by the denominator you have, e.g. 17/20 so you would divide 100 by 20 giving you an answer of 5. You now multiply the numerator and the denominator by 5, so you would end up with 85/100. The decimal would therefore be 0.85.

Although, in fractions this symbol, / , simply means divide. So you could use your calculator to figure out say 61/73 (61 divided by 73), which the answer would be 0.835616438 etc.

Hope that helped.

Answer 3

Converting from binary to decimal:

1. Write the binary digits in a column, least-significant bit first. Thus 10110100 would be written:

0 < least-significant bit

0

1

0

1

0

1

1 < most-significant bit

2. Multiply each digit by increasing powers of 2, starting with 2^0:

0 x 2^0 = 0 0 x 2^1 = 0

1 x 2^2 = 4

0 x 2^3 = 0

1 x 2^4 = 16

0 x 2^5 = 0

1 x 2^6 = 64

1 x 2^7 = 128

3. Sum the products:

128 + 64 + 0 + 16 + 0 + 4 + 0 + 0 = 212

Thus 10110100 binary is 212 decimal.

To reverse the process, repeatedly divide by 2 and take the remainder. Thus to convert 212 decimal to binary:

212 / 2 = 106 r 0

106 / 2 = 53 r 0

53 / 2 = 26 r 1

26 / 2 = 13 r 0

13 / 2 = 6 r 1

6 / 2 = 3 r 0

3 / 2 = 1 r 1

1 / 2 = 0 r 1

Read the remainders in reverse order (bottom up): 11010100

Answer 4

write the binary number

just below binary number digit write their place value such as 1,2,4,8,16,32,64......... starting from right to left.

in case zero appears in the last position , ignore the decimal value for that position

to get decimal equivalent add the remaining weights.

for example 111.101

Binary number 1 1 1 . 1 0 1

Place value of

decimal position 22 21 20 . 2-1 2-2 2-3

4 2 1 1/2 1/4 1/8

Answer 5

First forgot negative sign and convert decimal number to binary and then make it's 2's compliment. It will give you exactly binary number of that negative decimal number.

Answer 6

I am not sur my friend.

Answer 7

Convert the decimal fraction 1/2 to