Computing with binary numbers

• Before we can look at more powerful error correction codes, we need to look at some basic ways of computing with binaries.
• The following four operations with binary numbers are elementary.
  • XOR (exclusive or)

    a	b	a $\oplus$ b
    0	0	0
    0	1	1
    1	0	1
    1	1	0

  • OR

    a	b	a + b
    0	0	0
    0	1	1
    1	0	1
    1	1	1

  • AND

    a	b	a $\cdot$ b
    0	0	0
    0	1	0
    1	0	0
    1	1	1

  • NOT (inverse)

    a	$\bar{\mbox{a}}$
    0	1
    1	0

• The XOR operation is particularly important in connection with error correction coding.