Show Menu
Cheatography
  1. Home >
  2. Programming >

do not use Cheat Sheet (DRAFT) by

lmaolmaolmaolmaolmao

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Positional Number System

- Radix - number of unique symbols in a number system
- usually 0-9, then A-Z

Number System Base conversion

2x vs 10y

- Binary prefix are mainly use in memory capacity
- SI prefix are usually use in data transfer rate or storage space

- abbrev­iation * value = number of bits

Binary Data Organi­zation

• a bit has 2 cells

• most signif­icant (left) ------ least signif­icant (right)
• bit(b), byte(B)

• little endian - top address to bottom
• big endian - bottom address to top

Integer repres­ent­ation

UNSIGNED
0 to (2n)-1
normal
fill the rest with 0 (MSb)
SIGNED
-(2n-1) to +(2n-1)-1
sign and magnitude
sign bit | positive int
1's complement (n-1's)
flip for negative int
2's complement (n's)
flip then + 1, for negative int
- unsigned integers use zero extension
- signed integers use sign extension
in short, extend the MSb until you have reached the sufficient num of bits

integer operation overflow

SHOULD ___; otherwise, overflow

ADDITION
 ­ UNSIGNED SHOULD NOT have carry
 ­ SIGNED [same sign] SHOULD remain the same sign
 ­ SIGNED [different sign] add using 2's complement repres­ent­ation (never overflow)
SUBTRA­CTION
 ­ UNSIGNED SHOULD HAVE carry
 ­ SIGNED A-B = A+B' (2's complement B)
addition of signed integers [same sign]
 ­ 1. first bit should never change
 ­ 2. ignore carry if there is

IEEE 754 Floating point for single precision

1 - sign bit
8 - exponent
23 - mantissa
0 for positive
e' = e + 127
f in 1.f notation
Example:
Given: 3.5₁₀
 ­ 1. 3.5₁₀ = 11.1₂
 ­ 2. 1.11 x 21
 ­ 3. e' = 128₁₀ == 1000_0000₂
 ­ ­Answer: 1_1000­000_110 0000...00000

IEEE 754 Floating point for single precision

1 - sign bit
8 - exponent
23 - mantissa
0 for positive

test

1 - sign bit
8 - exponent
23 - mantissa
0 for positive
e' = e + 127
f in 1.f notation
Example:
Given: 3.5₁₀
­ 1. 3.5₁₀ = 11.1₂
­ 2. 1.11 x 21
­ 3. e' = 128₁₀ == 1000_0000₂
­ ­Answer: 1_1000­­00­0_110 0000...00000

Special cases floating single precision