By James L. Peterson and Werner Rheinboldt (Auth.)

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19. 20. 21. 22. 23. 24. -93 -13 -14 47 128 -128 0 -0 What range of numbers can be represented in 8 bits with an excess-3 notation? Write all possible bit patterns for a three-bit word. Interpret each of these bit patterns as a signed number in sign and magnitude, two's complement, ones' complement, and excess-4 notation, and also as unsigned numbers. What is an end-around carry? Why is it needed? How can a number represented in n bits be transformed into the same number, but represented in 2n bits?

Thus, each character needs seven or eight bits (depending upon whether or not parity is used). Each character is punched as a set of holes across the width of the tape, one bit per channel. For each character, a sprocket hole is also punched. The sprocket hole thus defines when a character should be looked for. Without the sprocket holes, a sequence of NULL characters with an ASCII code of 00000000 (with even parity) would be just a space of blank tape, and it would be difficult to determine how many NULL characters are on the tape.

Also, we see that the result has more bits than the original operands. Since we cannot store these bits (having only a fixed number of bits per word), something must be done with them. One approach is to just ignore them. 100100010 x 25 (truncated to nine bits for the fractional part). Truncation always results in a number which is less than or equal to the correct answer (in absolute value). Hence any inaccuracy in computation caused by the limited number of bits used to represent numbers tends to accumulate, and the accu­ racy of the result of repeated operations may be quite limited.

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