In this week you will:
- Learn conversion between BIN, OCT, DEC and HEX (during the class).
- Learn binary addition and subtraction.
- Do some exercise (homework).
Rules of Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, and carry 1 to the next more significant bit
For example,
00011010 + 00001100 = 00100110 | 1 1 | carries | ||
0 0 0 1 1 0 1 0 | = | 26(base 10) | ||
+ 0 0 0 0 1 1 0 0
|
= | 12(base 10) | ||
0 0 1 0 0 1 1 0 | = | 38(base 10) | ||
00010011 + 00111110 = 01010001 | 1 1 1 1 1 | carries | ||
0 0 0 1 0 0 1 1 | = | 19(base 10) | ||
+ 0 0 1 1 1 1 1 0
|
= | 62(base 10) | ||
0 1 0 1 0 0 0 1 | = | 81(base 10) |
Rules of Binary Subtraction
- 0 - 0 = 0
- 0 - 1 = 1, and borrow 1 from the next more significant bit
- 1 - 0 = 1
- 1 - 1 = 0
For example,
00100101 - 00010001 = 00010100 | 0 | borrows | ||
0 0 1 10 0 1 0 1 | = | 37(base 10) | ||
- 0 0 0 1 0 0 0 1
|
= | 17(base 10) | ||
0 0 0 1 0 1 0 0 | = | 20(base 10) | ||
00110011 - 00010110 = 00011101 | 0 10 1 | borrows | ||
0 0 1 1 0 10 1 1 | = | 51(base 10) | ||
- 0 0 0 1 0 1 1 0
|
= | 22(base 10) | ||
0 0 0 1 1 1 0 1 | = | 29(base 10) |