binary

Addition using Bitwise Operations

float binary represent

1. integer vs float

   1. integer: for n>0 { n = n%2 }: Get remainder circularly

      1: 00 00 00 00

   2. float: for n>0{ n= GetFloatPart(n*2) }: get decimal circularly

      0.75 : 0.11

   float binary represent maybe ultimate; 0.1= (0.00011…0011)

2. IEEE 754 a standard for represent float value;

   [sign 1bit][exponent 11bit][float 52bit]

   a = (-1)^sign *2^(exponent-1023)(float);

   2.1= 10.00011…0011 = (-1)^0 * 2^ 1024-1023)(00011..0011)

3. compare float

   1. math.Abs(1.1 - 1.2) <= 1e-9;

represent of positive and negative integer value

1. origin

   1: 0 0 00 00 01;

   -1: 1 0 00 00 00;

2. One’s Complement(反码)

   1: 00 00 00 01 = origin

   -1: 11 11 11 10 = origin Reverse except First bit

   1-1: 11 11 11 11 = -0

   cons: have two types of 0’s represent: 00000000 and 11111111

3. two’s complement(补码)

   1: 0 0 00 00 01 = origin

   -1: 1 1 11 11 11 = origin Reverse except First bit And add 1;

   1-1:0 0 00 00 00

bit operator

bitwise addition

//todo?

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def Bitwise_add(a,b):
    while b != 0:
        carry = a&b # Carry value is calculated 
        a = a^b # Sum value is calculated and stored in a
        b = carry<<1 # The carry value is shifted towards left by a bit

    return a # returns the final sum