"Everything in your computer is JUST BYTES."  --ajq

1 byte = 8 bits
Range (unsigned) of a byte is 0 to 255.

ON OUR PLATFORM
double is 8 bytes (64 bits)
float  is 4 bytes (32 bits)
You do not need to remember that.
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SCIENTIFIC NOTATION

base 10 scientific notation  (sign, mantissa, base, exponent)
0.375
 = 3.75 x 10⁻¹

3₁₀ x 2⁻³
 = 3₁₀ x ⅛
 = 11₂ x 2⁻³
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x/1gt  &d
  x/ is a command to examine memory
  1 is the # of those units (↓)
  g is the unit size; g is for 8 bytes ("giant word")
  t is the format; t is for binary bits
  ---
  &d means "address of d"

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5.505
0100000000010110000001010001111010111000010100011110101110000101
----+----1----+----2----+----3----+----4----+----5----+----6----

Goal:  Extract the sign, mantissa, and exponent from those bits.

----+----1----+----2----+----3----+----4----+----5----+----6----
0100000000010110000001010001111010111000010100011110101110000101
SEEEEEEEEEEEMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
│└────┬────┘└───────────────────────┬──────────────────────────┘
s  exponent                     mantissa
i
g
n

sign bit: 0 --- 0 means positve number; 1 means negative number; will multiply by (-1)^sign
exponent bits (×11): 10000000001 == 1025  -- subtract 1023 to get the real exponent: 2
mantissa bits (×52):  0110000001010001111010111000010100011110101110000101
                    1.↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑
                           0110000001010001111010111000010100011110101110000101
            mantissa = 1 + ────────────────────────────────────────────────────
                                                   2⁵²
                            0110000001010001111010111000010100011110101110000101
            mantissa =  1 + ─────────────────────────────────────────────────────
                           10000000000000000000000000000000000000000000000000000
                           1694479359798149 
            mantissa = 1 + ────────────────
                           4503599627370496

(-1)⁰ × ....... × 2⁽¹⁰²⁵⁻¹⁰²³⁾
4503599627370496

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POSITIONAL NOTATION (aka "decimal numbers")

Base 10 (decimal) positional notation

0.375
=   0 x 1         0 x 10⁰
    3 x 0.1       3 x 10⁻¹
    7 x 0.01      7 x 10⁻²
  + 5 x 0.001     5 x 10⁻³
= 375 x 0.001   375 x 10⁻³

Base 2 (binary) positional notation
=   0 x 1         0 x 2⁰
    0 x ½         0 x 2⁻¹
    1 x ¼         1 x 2⁻²
    1 x ⅛         1 x 2⁻³

=               11₂ x 2⁻³ = 3 x 1/8 = 0.375
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0.375 = a * 10^b  a and b are whole numbers.
0.33… = (can't ... but in base-3 we could)

5.505 = a * 10^b  a==375  b==-3
Can't do that in base-2.

5.505 == a x * 2^b