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HW01_sol

Ifyouusetheformulayouget2nwhichrequiresn1bits

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Unformatted text preview: e n rightmost bits for answer. **We’re assuming unsigned numbers here. If (1000)2 was signed, it would be considered a ‐8 instead of a +8. It would also be necessary to extend the leftmost bit when resizing. 2) Finding the 2’s Complement of a number is to perform the operation 2n‐x where x is the original number and n is the number bits used to store the number. Two’s Complement Representation is a hardware efficient scheme for supporting positive and negative numbers where finding the 2’s Complement is equivalent to multiplying by ‐1. Positive numbers are the same as unsigned binary (so long as the leftmost bit is ‘0’). Negative numbers are the 2’s Complement of the positive numbers. Note that finding the 2’s Complement of a number does not necessarily put it in 2’s Complement Representation. 3) 1.7) a) + + + + + (21)10 0 1 0 1 0 1 (11)10 + 0 0 1 0 1 1 (32)10 1 0 0 0 0 0 (10000)2s = (‐32)10 ≠ (32)10 Overflow must have occurred. Also notice that the 2 leftmost carry bits at the top are different. This only happens during overflow. b) 1 0 1 1 1 (‐14)10 (‐0 0 1 1 1 0) 1 1 0 0 1 0 (‐32)10 + (‐1 0 0 0 0 0) = + 1 0 0...
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