Hardware, Memory & Number Systems
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Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.
Memory units and conversions
Step multiplier
1\ \text{unit}_{next} = 2^{10} = 1024\ \text{units}_{prev}
KB->MB->GB->TB->PB all multiply by 1024
Byte identity
1\ \text{Byte} = 8\ \text{bits},\quad 1\ \text{Nibble} = 4\ \text{bits}
half a byte = nibble
Common ladders
1\ \text{GB} = 1024\ \text{MB} = 2^{20}\ \text{KB} = 2^{30}\ \text{B}
4 GB = 4096 MB = 2^22 KB
bits vs bytes
1\ \text{MB} = 8\ \text{Mb}
capital B = byte, small b = bit (speeds are usually bits)
Number systems: binary, octal, decimal, hexadecimal
Positional value
N = \sum d_i \cdot b^{i}
digit d_i at position i (from 0, rightmost), base b
Decimal to base b
N = (\ldots r_2 r_1 r_0)_b\ \text{from repeated division by } b
read remainders bottom to top
Grouping shortcuts
1\ \text{octal digit} \leftrightarrow 3\ \text{bits},\quad 1\ \text{hex digit} \leftrightarrow 4\ \text{bits}
group binary from the RIGHT; pad with leading zeros