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

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Overflow occurs in ones' complement if—and only if—the signs of the inputs are both the same and differ from the sign of the output. Another statement of this is that overflow occurs if there is a carry into the sign bit and no carry out of the sign bit (no end-around carry), or if there is no carry into the sign bit and there is a carry out (the carry out of the sign bit differs from the carry into the sign bit). Ones' complement allows simple arithmetic with negative numbers. It does suffer from one problem that sign and magnitude notation has: negative zero.

This is a set of switches which can be set to one of two positions (0/1) and can be read by the computer. It is often used to define addresses or contents of words. 4. A set of display lights, which can be used to display the contents of selected words of memory or registers. One light is provided for each bit in a word or address and indicates by its on /off state whether the corresponding bit is 1 or 0. 5. 3 THE I N P U T / O U T P U T S Y S T E M 6. whether the computer is running or halted, and perhaps other state information.

Why? Define a base 4 representation. Show how to convert from binary to base 4 and back. 4 can be used to convert from decimal to octal. Consider any three-digit number, abc. Show that abc represents a smaller number if it is interpreted as an octal number, as compared to interpreting it as a decimal number. That is, show that abc (base 8) < abc (base 10). Show that a binary number can be multiplied by 2 by shifting all bits left one bit. What should be shifted into the low-order bit, zero or one?

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