2 Let x be the value of the number formed by the rst 4 digit

2) Let x be the value of the number formed by the rst 4 digits of your LSUid and let y be the number formed by the last 4 digits of your LSUid. For example if you LSUid is 89-039-20115, then x = 8903 and y = 2015 (use this number for the problem). (a) Determine xy in sign magnitude, one’s complement and two’s complement. Use the minimum number of bits needed to represent xy as a signed number (b) Repeat the previous part for yx. (c) Represent each of the three strings you get in your answer to part (a) of this problem into octal and hexadecimal

Solution

4 bit decimal number can be represented in 15 bit (including 1 sign bit)

Part a:

Sign magnitude

x = 8903 = 010001011000111

y = 2015 = 000011111011111

x- y = 001101011101000₂ = 15350₈ = 1AE8₁₆

y - x = 101101011101000 = 55350₈ = 5AE8₁₆

1\'s complement form

x = 8903 = 010001011000111

y = 2015 = 000011111011111

x- y = 001101011101000₂ = 15350₈ = 1AE8₁₆

y - x = 110010100010111₂ = 62427₈ = 6517₁₆

1\'s complement form

x = 8903 = 010001011000111

y = 2015 = 000011111011111

x- y = 001101011101000₂ = 15350₈ = 1AE8₁₆

y - x = 110010100011000₂ = 62430₈ = 6518₁₆