Question

1. Use long division to convert decimal fraction into a binary expansion. 3/5

2. Find the decimal equivalent for the following binary numbers. 1101.11102

3. Use long division to convert decimal fraction into a binary expansion. 3/4

4. Find the binary equivalent the following decimal numbers. 14. 25390625 1

5. Find the decimal equivalent for the following binary numbers. 0.110001102

6. Exactly how many bytes are in the following? 60MB

Answer 1

1>

AS we can 3/5 is fraction number so we have to convert it into decimal form or float value

a=3/5

a=0.6

if we want to convert decimal fraction into binary then the digit after point is multiply by 2 till it repeat or become zero

0.6 x 2=1.2 (1 is integer part,0.2 is fractional part)

0.2 x 2=0.4   (0 is integer part,0.4 is fractional part)

0.4 x 2=0.8 (0 is integer part,0.8 is fractional part)

0.8 x 2=1.6 (1 is integer part,0.6 is fractional part)

0.6 x 2=1.2 (now the value is repeat so put bar in it)

(3/5)₁₀  =(0. 1001.......)₂

(3/5)₁₀  =(0.vinculum symbol(1001))

2> I think you write wrong question it must be (1101.1110)₂ convert in base 10

step 1>

binary	1	1	0	1	.(point)	1	1	1	0
power	1 x 23=8	1 x 22​​​=4	0 x 21=0	1 x 20=1		1 x 2-1=1/2	1 x 2-2​​​=1/4	1 x 2-3=1/8	0 x 2-4​​​​​​​=0

before point we multiply binary value with 2 power(index)

in decimal 8+4+0+1+1/2+1/4+1/8+0=(13.875) base 10 or in decimal

3>

S we can 3/4 is fraction number so we have to convert it into decimal form or float value

a=3/4

a=0.75

if we want to convert decimal fraction into binary then the digit after point is multiply by 2 till it repeat or become zero

0.75 x 2=1.5 (1 is integer part,0.5 is fractional part)

0.5 x 2=1.0 (1 is integer part,0.0 is fractional part)

  

(3/4)₁₀  =(0.11)₂

_{4> i was confuse with space in bits of question so i solve this}

_i>(14. 25390625 1)_{10 in binary}

14 / 2 = integer quotient 7 remainder is 0

7/2= integer quotient 3 remainder 1

3/2= integer quotient 1 remainder 1

when quotient is equal to 1 then write in reverse order 1110.

if we want to convert decimal fraction into binary then the digit after point is multiply by 2 till it repeat or become zero

0.253906251 x 2=0.507812502 (0 is integer part,0.507812502 is fractional part)

0.507812502 x 2=1.015625004 (1 is integer part,0.015625004  is fractional part)

0.015625004 x 2=0.031250008 (0 is integer part,0.031250008  is fractional part)

0.031250008 x 2=0.062500016 (0 is integer part,0.062500016 is fractional part)

0.062500016   x 2=0.125000032 (0 is integer part,0.125000032 is fractional part)

0.125000032 x 2=0.250000064 (0 is integer part,0.250000064   is fractional part)

0.250000064 x 2=0.500000128 (0 is integer part,0.500000128 is fractional part)

0.500000128    x 2=1.000000256 (1 is integer part,0.000000256   is fractional part)

now the value is approx equal so we write top to bottom

(14. 25390625 1))₁₀  =(1110.01000001)₂

_5>

binary	point	1	1	0	0	0	1	1	0
2* power(index)=decimal		1 x 2-1=1/2	1 x 2-2=1/4	0 x 2-3=0	0 x 2-4=0	0 x 2-5=0	1 x 2-6=1/64	1 x 2-7=1/128	0 x 2-8=1/256

sum of decimals=1/2+1/4+0+0+0+1/64+1/128+0=(0.7734375)₁₀

6> 1 kilobyte=1000 bytes, 1 megabyte =1000 kilobyte

so 60 MB == 60,000 KB

so 60,000 KB== 60 x 10⁶ bytes 1 mb == 10⁶ bytes

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