what this “if(k.c[3] & c)” part of code doing?

Question

#include<stdio.h>
#include<iostream.h>
main()
{
  unsigned char c,i;
  union temp
  {
    float f;
    char c[4];
  } k;
  cin>>k.f;
  c=128;
  for(i=0;i<8;i++)
  {
    if(k.c[3] & c) cout<<'1';
    else cout<<'0';
    c=c>>1;
  }
  c=128;
  cout<<'\n';
  for(i=0;i<8;i++)
  {
    if(k.c[2] & c) cout<<'1';
    else cout<<'0';
    c=c>>1;
  }
  return 0;
}

Answer 1

Bitwise Operation in your code

c = 128 therefore the binary representation is

c = 10000000

a & c will and every i^th but if c with evert i^th bit of a. Because c only has 1 in the MSB position (pos 7), so a & c will be non-zero if a has a 1 in its position 7 bit, if a has a 0 in pos bit, then a & c will be zero. This logic is used in the if block above. The if block is entered depending upon if the MSB (position 7 bit) of the byte is 1 or not.

Suppose a = ? ? ? ? ? ? ? ? where a ? is either 0 or 1 Then

a = ? ? ? ? ? ? ? ? 
AND & & & & & & & &
c = 1 0 0 0 0 0 0 0
    ---------------
    ? 0 0 0 0 0 0 0

As 0 & ? = 0. So if the bit position 7 is 0 then answer is 0 is bit position 7 is 1 then answer is 1.

In each iteration c is shifted left one position, so the 1 in the c propagates left wise. So in each iteration masking with the other variable you are able to know if there is a 1 or a 0 at that position of the variable.

Use in your code

You have

union temp
{
  float f;
  char c[4];
} k;

Inside the union the float and the char c[4] share the same memory location (as the property of union). Now, sizeof (f) = 4bytes) You assign k.f = 5345341 or whatever . When you access the array k.arr[0] it will access the 0th byte of the float f, when you do k.arr[1] it access the 1st byte of the float f . The array is not empty as both the float and the array points the same memory location but access differently. This is actually a mechanism to access the 4 bytes of float bytewise. NOTE THAT k.arr[0] may address the last byte instead of 1st byte (as told above), this depends on the byte ordering of storage in memory (See little endian and big endian byte ordering for this)

               Union k
+--------+--------+--------+--------+   --+
| arr[0] | arr[1] | arr[2] | arr[3] |     |
+--------+--------+--------+--------+     |---> Shares same location (in little endian)
|              float f              |     |
+-----------------------------------+   --+

Or the byte ordering could be reversed

               Union k
+--------+--------+--------+--------+   --+
| arr[3] | arr[2] | arr[1] | arr[0] |     |
+--------+--------+--------+--------+     |---> Shares same location (in big endian)
|              float f              |     |
+-----------------------------------+   --+

Your code loops on this and shifts the c which propagates the only 1 in the c from bit 7 to bit 0 in one step at a time in each location, and the bitwise anding checks actually every bit position of the bytes of the float variable f, and prints a 1 if it is 1 else 0.

If you print all the 4 bytes of the float, then you can see the IEEE 754 representation.

Answer 2

if(k.c[2] & c)

That is called bitwise AND.

Illustration of bitwise AND

   //illustration : mathematics of bitwise AND
   a = 10110101 (binary representation)
   b = 10011010 (binary representation)

   c = a & b 
     = 10110101 & 10011010 
     = 10010000 (binary representation)
     = 128 + 16 (decimal)
     = 144 (decimal)

Bitwise AND uses this truth table:

X | Y | R = X & Y
---------
0 | 0 | 0
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1

See these tutorials on bitwise AND:

• Bitwise Operators in C and C++: A Tutorial
• Bitwise AND operator &

Answer 3

A bitwise operation (AND in this case) perform a bit by bit operation between the 2 operands. For example the & :

11010010 &
11000110 =
11000010

Answer 4

c has single bit in it set. 128 is 10000000 in binary. if(k.c[2] & c) checks if that bit is set in k.c[2] as well. Then the bit in c is shifted around to check for other bits.

As result the program is made to display the binary representation of float it seems.