HEX 101 math

INTRODUCTION TO HEX

Hex 101 - base numbers overview

-hex is a base 16 expression of numberical values.
regular numbers are base 10, i.e. 1 10 20 30 40 (decimal).
hex was derived from binary coded decimal (BCD)

binary coded decimal placement bit value
8 4 2 1
--------
1 1 1 1 = 15
F = 15
F = 1 1 1 1 binary

hex characters
0 1 2 3 4 5 6 7 8 9 A B C D E F

hex numerical value equavalent
0 - 9 = 0 - 9
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
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byte = 8 bits
byte of hex FF example
FF = 255 decimal (unsigned; no negative or algebraic numbers)
FF = 1111 1111 binary

0F = 15 decimal
0F = 0000 1111 binary

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word OF hex 16 bits or 2 Bytes
FF FF
1111 1111 1111 1111 binary
usigned decimal
FFFF = 65535 dec
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so hex values weight are give by the least on the very right
to the most to the farther left.
opposite of decimal values

; why? because hex was derived from binary and the fact is
binary is weighted the same way.

binary bit values are in the format of 2 ^ n (POWER OF 2 )
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
AND SO ON...
bit placement values
512 256 128 64 32 16 8 4 2 1

binary
0010 0000 0000 = 512

02 00 hex = 512

note
0010 = 2 in hex
but sence the 02 hex is farther left in 0x0200h the decimal
weight value is greater equaling 512 decimal
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binary brief ( nibble = 4 bits) to HEX
0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
1010 = A
1011 = B
1100 = C
1101 = D
1110 = E
1111 = F

bits are added to total sum
-----------------------
ascii and hex dec character equavalents


end of indroduction.

 

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