Computer Organization and Architecture Tutorial 5 Kenneth Lee.

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Computer Organization and Architecture Tutorial 6 Kenneth Lee.

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Computer Organization and Architecture Tutorial 5 Kenneth Lee

+18 = (sign magnitude, 8 bits) +18 = (sign magnitude, 16 bits) −18 = (sign magnitude, 8 bits) −18 = (sign magnitude, 16 bits) +18 = (twos complement, 8 bits) +18 = (twos complement, 16 bits) −18 = (twos complement, 8 bits) −18 = (twos complement, 16 bits)

Boolean complement

−8 = 1000 (twos complement, 4 bits) The twos complement of 1000 is

Definition of XOR: XOR(0,0)=0; XOR(1,1)=0; XOR(0,1)=1; XOR(1,0)=1;

Example: Twos complement, 4 bits (-2~1) (1) Carry into the leftmost:0; Carry out of the leftmost:0; XOR(0,0)=0; There is no overflow. (0+1=1) (2) Carry into the leftmost:1; Carry out of the leftmost:0; XOR(1,0)=1; There is a overflow. (1+1=−2)

(3) Carry into the leftmost:0; Carry out of the leftmost:1; XOR(0,1)=1; There is a overflow. (-2-1=1) (4) Carry into the leftmost:1; Carry out of the leftmost:1; XOR(1,1)=0; There is no overflow. (-1-1=-2)

Example: (1)1-digit numbers, base 10 9∙9=81 (2) 2-digit numbers, base 2 11∙11=1001 Notation: n-digit number base 2 is different with their twos complement! The max of a n-digit base 2 number is 2 n -1, but the max of a n-digit twos complement is 2 n-1 -1

a.Memory cycle time = = 100 ns data rate = 1 bit/100 ns = 10,000,000 bits/s = 10 Mbps b.32*10 = 320 Mbps = 40 MB/s