Numeral systems

Hex(16) Bin(2) Dez(10)
0 0000 00
1 0001 01
2 0010 02
3 0011 03
4 0100 04
5 0101 05
6 0110 06
7 0111 07
8 1000 08
9 1001 09
A 1010 10
B 1011 11
C 1100 12
D 1101 13
E 1110 14
F 1111 15
-- -- --
10000 16
100000 32
1000000 64
10000000 128

HEXADEZIMAL SYSTEM

a(2)) 1111 1110 1010
a(10)) 15*162 + 14*16 + 10 = 4.074

b(2)) 1010 1111 1111 1110
b(10)) 10*163 + 15*162 + 15*16 + 14 = 45.054

c(2)) 0001 1010 0001 1010
c(10)) 1*163 + 10*162 + 1*16 + 10 = 6.682

d(2)) 0001 1111 1010 1111 1010 0001
d(10)) 1*165 + 15*164 + 10*163 + 15*162 + 10*16 + 1 = 2.076.577

e(2)) 0001 0000 0001 0000 0101 0100
e(10)) 1*165 + 0*164 + 1*163 + 0*162 + 5*16 + 4 = 1.052.756

f(2)) 0100 0101 0111 1000 1011 1111 1110
f(10)) 4*166 + 5*165 + 7*164 + 8*163 + 11*162 + 15*16 + 14 = 72.846.334


BINARY SYSTEM

a(16)) 14AF
a(10)) 1*163 + 4*162 + 10*16 + 15 = 5.295

b(16)) 8FFE
b(10)) 8*163 + 15*162 + 15*16 + 14 = 36.862

c(16)) D640
c(10)) 13*163 + 6*162 + 4*16 + 0 = 54.848

d(16)) 35F8
d(10)) 3*163 + 5*162 + 15*16 + 8 = 13.816

e(16)) 3291
e(10)) 3*163 + 2*162 + 9*16 + 1 = 12.945

DECIMAL SYSTEM

32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1 HEX(16)
a(2) 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 3039
b(2) 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 8712
c(2) 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 1 324F
d(2) 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 B337
84.769/16 = 5.298 → 5.298 x 16 = 84.768 → 84.769 - 84.768 = 1
5.298/16 = 331 → 331 x 16 = 5.296 → 5.298 - 5.296 = 2
331/16 = 20 → 20 x 16 = 320 → 331 - 320 = 11
20/16 = 1 → 1 x 16 = 16 → 20 - 16 = 4
1/16 = 0 → 0 x 16 = 0 → 1 - 0 = 1
HEX(16) = 14B21
BIN(2) = 0001 0100 1011 0010 0001
1.111.111/16 = 69.444 → 69.444 x 16 = 1.111.104 → 1.111.111 - 1.111.104 = 7
69.444/16 = 4.340 → 4.340 x 16 = 69.440 → 69.444 - 69.440 = 4
4.340/16 = 271 → 271 x 16 = 4.336 → 4.340 - 4.336 = 4
271/16 = 16 → 16 x 16 = 256 → 271 - 256 = 15
16/16 = 1 → 1 x 16 = 16 → 16 - 16 = 0
1/16 = 0 → 0 x 16 = 0 → 1 - 0 = 1
HEX(16) = 10F447
BIN(2) = 0001 0000 1111 0100 0100 0111
0
0

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