Arrange the following in descending order?

all are hexadecimal representations of 16bit signed integers (2's complement system):

3EEE 8000 DEED 7012 FFFE 0644 FF00

I know that 8000 is the most negative since it is 1000000000000000 in binary and the 1 indicates it is the largest negative number, but I don't understand how to convert a 2's complement hex number to the proper negative or positive decimal number to tell which order these numbers go in...can anyone explain?

each letter represents 4 bits. So any number that begins with 8-F is negative

You can convert the numbers like so

hex binary
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111

To convert the number to binary each hex digit represents 4 bits.

so

DEED = 1101:1110:1110:1101

to get the magnitude convert this number to its positive representation. flip the bits and add 1

1101:1110:1110:1101

0010:0001:0001:0010
+ 0000:0000:0000:0001
------------------------------------
0010:0001:0001:0011

Converting back to Hex using the binary representation for each number
: 2: 1: 1: 2

so DEED = - 2112

hope this helps.

-- edit --
You do not need to convert to decimal to answer this question.

The simple way to convert hex to decimal is to multipy each digit by 16^n where n represents the position of the hexadecimal digit.

so ABCD = A(10) *16^3 + B(11) * 16^2 + C(13) * 16^1 + D(14) * 16^0

or simply (10 * 16^3) + (11 * 16^2) + (13 * 16^1) + (14 * 16^0) =40960 + 2816 +192 + 14
= 43982

what????

Hi there,

If you have Windows you can do this on the Calculator that comes with it.

Open the calculator and click on View, then select Scientific.

Tick the Hex selection, enter your hex code, then tick Bin (Binary). The binary conversion of the hex code will appear as the result display.

Good luck with it!

Directly converting a hexadecimal number to a 2's complement binary number can be difficult... So first convert the hexadecimal number to binary and then to decimal...and after that you can arrange it in a descending order
Use the following table and convert the hexa decimal numbers to binary
0=0 0 0 0
1=0 0 0 1
2=0 0 1 0
3=0 0 1 1
4=0 1 0 0
5=0 1 0 1
6=0 1 1 0
7=0 1 1 1
8=1 0 0 0
9=1 0 0 1
A=1 0 1 0
B=1 0 1 1
C=1 1 0 0
D=1 1 0 1
E=1 1 1 0
F=1 1 1 1
Replace each Hexa digit by the binary in the table...

3EEE=(binary of 3) (binary of E)(binary of E) (binary of E)
...... ... (0 0 1 1)...(1 1 1 0)...(1 1 1 0)...(1 1 1 0 )
3EEE=0011111011101110
convertint this to decimal is use of normal procedure....
starting from the least significant bit
0 x 2^0 + 1x 2 ^1+....+0 x 2^15 = 16110

If the most significant bit (left most bit in a binary number of 16 bits) is 1 then ignore that bit and
subtract 1 from the result... flip the bits in the result from subtraction and convert it to decimal using the method mentioned above.... result is a positive number....but because you have got a 1 in the most significant bit position it becomes a negative number