Question

Convert the following numbers as directed (i) Decimal 257.125 into binary and hexadecimal ​

Answer 1

Answer:

$(257.125)_{10}=(100000001.0010)_{2}$

$(257.1 25)_{10}=(101.2)_{16}$

Step-by-step explanation:

To convert decimal into binary when the number is greater than one,divide the number by 2 and kept the remainder

$\begin {array}{r |1}</p><p>2&257\:\:\:\:\:\:1\\</p><p>\cline{2-2}2&128\:\:\:\:\:\:0\\</p><p>\cline{2-2}2&64\:\:\:\:\:\:0\\</p><p>\cline{2-2}2&32\:\:\:\:\:\:0\\</p><p>\cline{2-2}2&16\:\:\:\:\:\:0\\</p><p>\cline{2-2}2&8\:\:\:\:\:\:0\\</p><p>\cline{2-2}2&4\:\:\:\:\:\:0\\</p><p>\cline{2-2}2&2\:\:\:\:\:\:0\\</p><p>\cline{2-2}&1</p><p>\end{array}$

So,

$(257)_{10}=(100000001)_{2}$

For numbers less than 1,multiply that number by 2

0.125×2=0.250 before decimal point 0

0.250×2=0.500 before decimal point 0

0.500×2=1.00 before decimal point 1

0.00×2 =0.00 before decimal point 0

so,$(.125)_{10}=(0010)_{2}\\\\(257.1 25)_{10}=(100000001.0010)_{2}$

Step2: Hexadecimal conversion

Make pair of 4 binary numbers

$(0001\:\:\:0000\:\:\:0001.0010)_{2}=(101.2)_{16}$

just put the Hexadecimal code of that four-2 pairs

Hope it helps you.

Answer 2

Step-by-step explanation: