Binary Arithmetic

This lesson covers binary addition, binary subtraction using two's complement, overflow, and bit shifting (logical and arithmetic shifts). These are core skills for the OCR H446 specification.

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Binary Addition

Binary addition follows the same rules as denary addition, but with only two digits (0 and 1).

Addition Rules

A	B	Sum	Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

When both bits are 1, the sum is 0 and the carry is 1 (just like 1+1=2 in denary, which is "10" in binary).

If there is also a carry-in of 1: 1 + 1 + 1 = 1 with carry 1.

Worked Example: 01101011 + 00110101

  Carry:  1 1 1 1 1 1
          0 1 1 0 1 0 1 1   (107)
        + 0 0 1 1 0 1 0 1   ( 53)
        ─────────────────
          1 0 1 0 0 0 0 0   (160)

Verification: 107 + 53 = 160. Correct.

Worked Example: 11111111 + 00000001