Question 1190115: Convert the following unsigned 8 bit binary numbers into both hex and decimal
a. 00110110 base 2
b. 00111101 base 2
c. 01111100 base 2
Can you please explain this homework question step-by-step? Thank you!
Found 2 solutions by Alan3354, math_tutor2020:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Convert the following unsigned 8 bit binary numbers into both hex and decimal
a. 0011 0110 base 2 = 36H = 3*16 + 6 = 54
b. 0011 1101 base 2 = 3DH = 3*16 + 13 = 61
c. 0111 1100 base 2 = 7CH = 7*16 + 12 = 124
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
I'll go over part (a) to get you started.
Let's convert this base 2 value
0011 0110
into base 10, aka decimal
To start off, we'll just focus on the last set of four values 0110
Any four digit number like this has the template of
abcd base 2 = (a*2^3 + b*2^2 + c*2^1 + d*2^0) base 10
So,
0110 base 2 = (0*2^3 + 1*2^2 + 1*2^1 + 0*2^0) base 10
0110 base 2 = 6 base 10
Effectively it's like saying
0110 base 2 = 2^2+2 base 10 = 4+2 base 10 = 6 base 10
The middle '1's are switches that flip on to add the 2^2 and 2^1 terms. The 0s mean we don't add those other powers of 2.
Through similar steps we will have
0011 base 2 = 3 base 10
Now if we were to multiply by 16, then that's the same as tacking four 0's at the end of the binary number (this works because 2^4 = 16)
So,
0011 0000 base 2 = (3 base 10)*(16 base 10)
0011 0000 base 2 = 48 base 10
Lastly,
(0011 0000 base 2) + (0110 base 2) = (48 base 10) + (6 base 10)
0011 0110 base 2 = 54 base 10
You can use a calculator like this
https://www.binaryhexconverter.com/binary-to-decimal-converter
to help confirm the answer
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The hexadecimal numbering system goes from 0 to F
The 0 to 9 work the same in base 10
The A through F are the 6 extra values to get 10+6 = 16 items total
A base 16 = 10 base 10
B base 16 = 11 base 10
C base 16 = 12 base 10
D base 16 = 13 base 10
E base 16 = 14 base 10
F base 16 = 15 base 10
Once we reach number F, the next number is 10
F base 16 = 15 base 10
10 base 16 = 16 base 10
11 base 16 = 17 base 10
12 base 16 = 18 base 10
and so on
Notice that once we reach the end of the digits in our base 16 system, we add on another slot and reset things back to zero so to speak.
Hopefully this helps clear up any confusion of how the hexadecimal system works.
Anyways, let's convert the binary number 0011 0110 to hexadecimal
0011 base 2 = 3 base 10
0110 base 2 = 6 base 10
Since both values (3 and 6) are smaller than 10, this means we won't use letters A through F.
So,
0011 0110 base 2 = 36 base 16
Here's a free calculator to help check your work
https://www.binaryhexconverter.com/binary-to-hex-converter
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