Overview
This lecture explains how to perform addition and subtraction using two's complement notation, including handling positive and negative binary numbers and interpreting results.
Two's Complement Addition for Positive Numbers
- For positive numbers, use standard binary addition; no changes needed.
- Example: 3 (0011) + 4 (0100) = 7 (0111).
Addition and Subtraction Involving Negative Numbers
- To represent a negative number in two’s complement, invert all bits of the number and add one.
- Example: To find -6 in four bits, take 6 (0110), flip bits (1001), add 1 → (1010).
- Add positive and negative binary numbers directly, then interpret the result.
Interpreting the Result
- If the most significant bit (MSB) of the result is 0, the answer is positive; keep the binary value as is.
- If the MSB is 1, it’s negative; to find the decimal value, flip all bits and add one.
- Ignore any carry out beyond the number of bits used.
Example Calculations
- +5 (0101) + (-6) (1010) = (1111), MSB is 1 → flip bits (0000), add 1 → (0001) = -1.
- -5 (1011) + 6 (0110) = (0001), MSB is 0 → answer is +1.
- 23 (010111) - 6 (111010): After aligning bit widths and addition, ignore carry out; positive result with MSB 0.
Key Terms & Definitions
- Two’s Complement — A method to represent negative numbers in binary by inverting bits and adding one.
- MSB (Most Significant Bit) — The leftmost bit in a binary number; indicates sign (0 for positive, 1 for negative).
- Carry Out — Any extra bit produced after the final addition; ignored in two’s complement.
Action Items / Next Steps
- Practice converting positive integers to two’s complement negative form.
- Complete assigned homework problems on two’s complement addition and subtraction.