This implies that the machine can use a single type

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Unformatted text preview: Ü · Ý ¾Û . This case is referred to as positive overflow. We have added Û ½ two positive numbers Ü and Ý (that’s the only way we can have Þ ¾ ) and obtained a negative ¼¼ Ü · Ý ¾Û . result Þ ¾ Û ½ Þ ¾ Û By the preceding analysis, we have shown that when operation +tÛ is applied to values Ü and Ý in the range ¾Û ½ Ü Ý ¾Û ½ ½, we have Ü+ Ý t Û Ü·Ý ¾ Ü·Ý Ü·Ý·¾ Û Û ½ Ü · Ý ¾ ½ Ü · Ý Ü · Ý ¾ ½ ¾ Û Û Û ¾ Û ½ Normal Positive Overflow (2.12) Negative Overflow Figure 2.19 illustrates two’s complement addition for word size Û . The operands range between and . When Ü · Ý , two’s complement addition has a negative underflow, causing the sum to be incremented by 16. When Ü·Ý , the addition yields Ü · Ý . When Ü · Ý , the addition has a positive overflow, causing the sum to be decremented by 16. Each of these three ranges forms a sloping plane in the figure. Equation 2.12 also lets us identify the cases where overflow has occurred. When both Ü and...
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