Computer Organization and Architecture

Tutorial 5

Kenneth Lee

+18 = 00010010 (sign magnitude, 8 bits)+18 =0000000000010010 (sign magnitude, 16 bits)−18 = 10010010 (sign magnitude, 8 bits)−18 =1000000000010010 (sign magnitude, 16 bits)

+18 = 00010010 (twos complement, 8 bits)+18 =0000000000010010 (twos complement, 16 bits)−18 = 11101110 (twos complement, 8 bits)−18 =1111111111101110 (twos complement, 16 bits)

Boolean complement

−8 = 1000 (twos complement, 4 bits)

The twos complement of 1000 is 1000 0111 + 1

1000

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)-2 -1 0 110 11 00 01

(1) 00 +01 01Carry into the leftmost:0; Carry out of the leftmost:0;XOR(0,0)=0; There is no overflow. (0+1=1)

(2) 01 +01 10Carry into the leftmost:1; Carry out of the leftmost:0;XOR(1,0)=1; There is a overflow. (1+1=−2)

(3) 10 +11 101Carry into the leftmost:0; Carry out of the leftmost:1;XOR(0,1)=1; There is a overflow. (-2-1=1)

(4) 11 +11 110Carry 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 2n-1, but the max of a n-digit twos complement is 2n-1-1

a. Memory cycle time = 60 + 40 = 100 ns data rate = 1 bit/100 ns = 10,000,000 bits/s = 10 Mbpsb. 32*10 = 320 Mbps = 40 MB/s