Convert the following decimal numbers to BINARY and HEXADECIMAL numbers. a) 0.37
ID: 3663610 • Letter: C
Question
Convert the following decimal numbers to BINARY and HEXADECIMAL numbers.a) 0.375 (base 10) b)124.25 (base 10)
Convert the following binary numbers to HEXADECIMAL and DECIMAL numbers.
c) 0.001 (base 2) d) 11001.11 (base 2)
PLEASE HELP ME! I understand when the whole numbers need to be converted but the decimals after it throws me off. Please show some steps to make my life easier, thank you. Convert the following decimal numbers to BINARY and HEXADECIMAL numbers.
a) 0.375 (base 10) b)124.25 (base 10)
Convert the following binary numbers to HEXADECIMAL and DECIMAL numbers.
c) 0.001 (base 2) d) 11001.11 (base 2)
PLEASE HELP ME! I understand when the whole numbers need to be converted but the decimals after it throws me off. Please show some steps to make my life easier, thank you.
a) 0.375 (base 10) b)124.25 (base 10)
Convert the following binary numbers to HEXADECIMAL and DECIMAL numbers.
c) 0.001 (base 2) d) 11001.11 (base 2)
PLEASE HELP ME! I understand when the whole numbers need to be converted but the decimals after it throws me off. Please show some steps to make my life easier, thank you.
Explanation / Answer
Conversion of Decimal Fration to any Base:
First make two parts of Given Decimal Fraction Number
1. Integer Part
2. Decimal Part
For 124.25 -> Integer part is 124 Decimal part is 25
-------------------------------------------------------
Conversion of Integer Part - > 124
a. Divide by 2
b. Take 'Remainder' as the digit
c. take the 'Quotient' as the starting point for the next step
d. repeat steps a, b , and c until you get 'Quotient' to 0
e. read the number (Remainder) starting from the down
124 / 2 = 62 (Quotient) , 124 % 2 = 0 (Remainder) (LSB)
62 / 2 = 31 (Quotient) , 62 % 2 = 0 (Remainder)
31 / 2 = 15 (Quotient) , 31 % 2 = 1 (Remainder)
15 / 2 = 7 (Quotient) , 15 % 2 = 1 (Remainder)
7 / 2 = 3 (Quotient) , 7 % 2 = 1 (Remainder)
3 / 2 = 1 (Quotient) , 3 % 2 = 1 (Remainder)
1 / 2 = 0 (Quotient) , 1 % 2 = 1 (Remainder) (MSB)
so binary for 124 is (1111100)
Conversion of Decimal Part - > 124
a. Multiply by two
b. take decimal as the digit
c. take the fraction as the starting point for the next step
d. repeat until you either get to 0 or a periodic number
e. read the number starting from the top - the first result is the first digit after the comma
0.25 * 2 = 0.50 => Fraction Part = 50, Integer Part = 0 (MSB)
0.50 * 2= 1.00 => Fraction Part = 00, Integer Part = 1 (LSB)
here fraction part is 0, so STOP
hence binary of 0.25 is 0.01
For 0.375
0.375 * 2 = 0.750 -> 0
0.750*2 = 1.500 - > 1
0.500*2 = 1.000 - > 1
hence binary for 0.375 is 0.011
Conversion from Decimal to HEXADECIMAL
Steps are same , only difference is in BASE , use 16 for division or Multiplication instead of 2
for 0.375
0.375*16 = 6.00 -> 6
fraction becomes 0, so STOP
hexadecimal of 0.375 is 0.6
For 124.25 -> Integer part is 124 Decimal part is 25
for 124
(10- A, 11- B, 12- C, 13- D, 14- E, 15- F)
124 / 16 = 7 , 124%16 = 12, so C
7/16 = 0, 7%16 = 7
hence hexadecimal of 124 is 7C
for 25 (fraction part)
0.25*16 = 4.00 -> 4
fraction part becomes 0 , so STOP
hexadecimal of 0.25 is 0.4
hence hexadecimal for 124.25 is 7C.4
Conversion of Binary to Decimal:
for 0.001
Integer part = 0 , convert it in decimal or hexadecimal(as you know how to deal with integer part)
Fraction Part= 0.001
0.48 in decimal is the same as:
4 * 10^-1 + 8 * 10^-2
So for binary, if you had something like 0.001 it would be:
0 * 2^-1 + 0 * 2^-2 + 1 * 2^-3
then add both integer and fraction part
Conversion of Binary to HEXADECIMAL
First convert it in Decimal, as above explained
then Convert Decimal to Hexadecimal, as explained above