Convert hexadecimal number to bit?

drahcir321Bydrahcir321

Hi guys, I've been given this assignment and I'm just not sure what to do next. How do I convert it?

The hexadecimal number 0xA1 has the decimal value as

a) 8-bit unsigned:

b) 8-bit signed (2's complement):

c) 16-bit signed (2's complement):

d) 32-bit signed (2's complement):

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ultrarunner
ultrarunner
2 years ago

A1 = 1010 0001

  • That would be 161 (from 128+32+1) as 8-bit unsigned decimal.
  • The 8-bit two's complement is 01011111, which corresponds to -95 in decimal.
  • The 16-bit two's complement is 11111111 01011111, which corresponds to -65375 in decimal.
  • The 32-bit two's complement is 11111111 11111111 11111111 01011111, which in decimal form is -4294967135.
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drahcir321
Author
drahcir321
2 years ago
Reply to  ultrarunner

Hi, it's really nice of you to give me the answer. However, it's more important for me to understand the concept of conversion. How did you do it? A1 = 1010 0001, I understand that.

0
ultrarunner
ultrarunner
2 years ago
Reply to  drahcir321

In a) I added it anyway.

And for b) to d): Forming a two's complement means inverting all bits and then adding 1. The result can then be converted to the decimal system as usual (ie, adding all place values ​​containing a 1).

1
drahcir321
Author
drahcir321
2 years ago

Oh right, I missed that. Thanks so much!

0
ultrarunner
ultrarunner
2 years ago

Yes, that's right.

And since the problem says "decimal," you have to convert it.

1
drahcir321
Author
drahcir321
2 years ago

I think I understand now. I used a different number just to check. Would that be correct?

1D = 0001 1101

b)1110 0011

c) 11111111 11100011

d)11111111 11111111 11111111 11100011

Do I actually have to convert this to decimal notation?

0