- Sorry, I have no real good on line references. I am using Kumar for this.
- As we saw with 9's and 10's complment for base 10, we can perform addition and subtraction without the rules based system sign-magnitude requires.
- The equivelent system is 1's complement and 2's complement.
- This system
- Requires a fixed number of bits. So 3 bit 2's compliement for example.
- Like 9's complemnt and 10's complement we subtract from the radix-1 (remember 9) but in this case, we subtract from 1.
- This is equivelent to flip the bits
- 1-1 = 0
- 1-0 = 1
- Which, by the way, is a not gate!

- For 2's complement, add one.

- Examples:
- Find the 4 bit 1's and 2's complement of -4
- 4 = 0100
_{2} - -4 = 1011
_{2}in 1's complement notation - -4 = 1100
_{2}in 2's complement notation -
0100

_{2}=> 1011_{2}(a) 1011_{2}+1 = 1100_{2}(b)

- 4 = 0100
- What does the bit pattern 1010
_{2}represent in 1's complement and 2's complement?- 1010
_{2}is -5 in 1's complement - 1010
_{2}is -6 in 2's complement. -
1010

_{2}=> 0101_{2}= 5 0101_{2}+1 = 0110_{2}= 6

- 1010

- Find the 4 bit 1's and 2's complement of -4
- The trick is "flip the bits and add 1" for 2's complement.
- We have an indicator of the sign in both 1's and 2's complemnt
- if the msb is 0, the rest of the bits are the magnitude
- If the msb is 1, take the 1 or two's complement to find the magnitude

- This rule fails in one case for two's complement,
- for the bit pattern 10...0 in any number of bits.
- Assume 4 bits.
- 1000
_{2}-> 0111_{2}+1 -> 1000_{2} - In this case, it represents -2
^{-3}= -8