Convert (1011101)subscript2 to base 16.?

Question

Convert (1011101)2 to base 16.

The 2 is small or subscripted

Answer 1

101 1101 = 5D

Answer 2

first basic base facts.

base 10 means this

x*10^2 + y *10^1 + z * 10^0 etc..

so say 356 = 3 x 10^2 + 5 *10^1 + 6 * 10^0 = 300+50+6

base 2 means this

x*2^2 + y *2^1 + z * 2^0 etc..

so say 101 = 1 x 2^2 + 0 *2^1 + 1 * 2^0 = 4+0+1 = 5 base 10

base 16 means this

x*16^2 + y *16^1 + z * 16^0 etc..

so 947 base 16 = 9*16^2 + 4 *16^1 + 7 * 16^0 = 2304+64+7

ok?

couple more facts. base 10 we count from 0 to 9, (ie 10 -1) then put a 1 in the column to the left and start over. base 2, 0 to 1, then 1 to the left etc. base 16, need to count from 0 to 15. but that's two digits so we use A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15

so 9FA base 16 (aka hexadecimal) = 9 x 16^2 + 15 x 16^1+10 = 2304 + 240 + 10 base 10

all that said, there are two ways to work this problem.....

1) convert base 2 to base 10 then to base 16

1011101 = 1 x 2^6 + 0 x 2^5 + 1 x 2^4 + 1 x 2^3+ 1 x 2^2 + 0 x 2^1 + 1 x 2^0 = 64 + 0 + 16 + 8 + 4+ 0 + 1 = 93

93 base 10 to base 16 remember base 16 =

16^2 + 16^1 + 16^0 etc so 93 is

5 x 16 + 13 x 1 = 5D base 16

2) solution 2, my preferred method....


notice that with base 2, the right four digits, add up to 15. ie.

1111 base 2 = 1 x 8+ 1 x 4 + 1 x 2 + 1 x 1 = 15 ie (15 x 16^0)
also notice that 15 is F base 16. ie. the right four digits can be expressed as 1 character in base 16.

for base 2 number with 8 digits, the left four digits add to 240
ie 15 x 16^1.

ie. 11110000 is 1 x 2^7 + 1 x 2^6 + 1 x 2^5 + 1 x 2^4
= 128 + 64 + 32 + 16 = 240

if we had 4 more digits to the left they would add to 15 x 16^2

get it? starting from the right, group the numbers in sets of four and a zero to left when needed then convert each set of 4 independently...

ie if you have the number 1011101 base 2 thats

0101,1101

the left numbers add to 5, the right add to 13. so your hexadecimal number is 5D

101001110011101 base 2 is

0101,0011,1001,1101 =
5,3,9,13 or 539D base 16

Answer 3

1011101 base 2 means
1 + 2^2 + 2^3 + 2^4+2^6
= 1 +4 +8 + 16 + 64 = 93
which is 5*16 + 13

base 16 , we need single didgits, we need 5 for 5 *16^1, and to represent 13, we use 10=A, 11=B, 12 = C, 13 = D

5D means 5X16^1 + 13

answer 5D

Answer 4

The answer is 5d

You can use the built-in caculator in Windows to do this (set it to scientific mode)

alternatively, use the link below to convert from binary to hexadecimal

Answer 5

5D

If you want an explanation, just ask (in 'additional details' to your question)

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Answer 6

Hex is fun!!!