Review-Questions-on-Binary-Integer-Arithmetic

# Review-Questions-on-Binary-Integer-Arithmetic - Review...

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Revised 15 Nov 2004 Review Questions: Binary Integer Arithmetic © 2004 Charles Abzug 1. Indicate the decimal value associated with each of the given bit sequences, when the bit sequence is interpreted as an integer number in each of the following representations: a. Unsigned Numbers b. Signed-Magnitude Numbers c. Ones’-Complement Representation d. Two’s-Complement Representation e. Saturation Arithmetic f. Excess-2,047 g. Excess-2,048 (a) 101100111110 2 (b) 010010101100 2 (c) 110101110101 2 (d) 011100111010 2 (e) 101010101100 2 (f) 110000111010 2 (g) 111001111110 2 (h) 100110010101 2 (i) 001010011010 2 (j) 100011001100 2 2. Describe the algorithm for the addition of two Signed-Magnitude binary integers.

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Review Questions: Binary Digital Arithmetic Page 2 of 16 © 2004 Charles Abzug Revised 15 Nov 2004 3. Fill in the following table, showing the specified values for integer arithmetic of 10-bit numbers: Number Representation Range of Numbers Represented How many zeroes? Carry Bit represents Carry-Out from which bit in the Sum Register? How do you go about finding the representation of the negative of a number? Unsigned Numbers Signed-Magnitude Ones’-Complement Two’s-Complement Saturation Arithmetic Excess-511 Excess-512 Instructions for the Next Several Problems: Add each of the following pairs of binary numbers five times, following the rules of: a. Unsigned Numbers b. Signed-Magnitude Numbers c. Ones’-Complement Representation d. Two’s-Complement Representation e. Saturation Arithmetic In each case: (i) show the carry in for each bit; (ii) show the bit sequence that would appear in the Sum Register; (iii) indicate what is the decimal value represented by the bit sequence of the Augend; (iv) indicate what is the decimal value represented by the bit sequence of the Addend; (v) indicate what is the decimal value represented by the bit sequence that would appear in the Sum Register; (vi) indicate whether a 0 or a 1 would appear in the Carry Bit of the Status Register; (vii) indicate the value ( 0 or 1 ) that would appear in the Overflow Bit of the Status Register; and (viii) state whether or not the value of the bit sequence appearing in the Sum Register is the correct sum of the values of the numbers represented in the Augend and Addend Registers.
Review Questions: Binary Digital Arithmetic Page 3 of 16 © 2004 Charles Abzug Revised 15 Nov 2004 4. UNSIGNED INTEGERS Carry/Borrow Bits: Decimal Values: Z bit: Augend Register: 0 0 1 0 1 1 1 1 N bit: Addend Register: 0 1 0 0 1 1 1 0 C bit: S u m R e g i s t e r : V b i t : SIGNED-MAGNITUDE INTEGERS Carry/Borrow Bits: Decimal Values: Z bit: Augend Register: 0 0 1 0 1 1 1 1 N bit: Addend Register: 0 1 0 0 1 1 1 0 C bit: S u m R e g i s t e r : V b i t : ONES’-COMPLEMENT INTEGERS Carry/Borrow Bits: Decimal Values: Z bit: Augend Register: 0 0 1 0 1 1 1 1 N bit: Addend Register: 0 1 0 0 1 1 1 0 C bit: S u m R e g i s t e r : V b i t : TWO’S-COMPLEMENT INTEGERS Carry/Borrow Bits: Decimal Values: Z bit:

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## This note was uploaded on 05/04/2011 for the course CSC 330 taught by Professor Paterson during the Spring '11 term at Edison State College.

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Review-Questions-on-Binary-Integer-Arithmetic - Review...

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