1.(111 002 220)*3化为五进制
(111 002 220)*3=(3^8+3^7+3^6+2×3^3+2×3^2+2×3)*10=(9555)*10
=(3×5^5+5^3+2×5^2+5)*10=(301210)*5
2.(10 010)*2 除以 (110)*2 + (10 101)*2 除以(11)*2
=(11)*2+(111)*2
=(1010)*2
3.(100 100)*2 - (1 011)*2 乘以 (11)*2 + (11 011)*2
=(100 100)*2 - (100001)*2 + (11 011)*2
=(11)*2 + (11 011)*2
=(11110)*2
4.[(10 001 000 100)*2 - (100 010 001)*2] 除以(1 001)*2乘以 (11)*2
=(1100110011)*2除以(1 001)*2乘以 (11)*2
=(1 011011)*2乘以 (11)*2
=(100000001)*2
5.求证:在g大於或等於5时,(1 234 321)*g是平方式
在g大於或等於5时,(1 234 321)*g=1+2g+3g^2+4g^3+3g^4+2g^5+g^6
=(1+g)^2+2g^2+4g^3+3g^4+2g^5+g^6
=(1+g)^2+2g^2(1+2g+g^2)+g^4+2g^5+g^6
=(1+g)^2+2g^2(1+g)^2+g^4(1+2g+g^2)
=(1+g)^2+2g^2(1+g)^2+g^4(1+g)^2
=(1+g)^2(1+2g^2+g^4)
=(1+g)^2(1+g^2)^2
={(1+g)(1+g^2)}^2
=(1+g+g^2+g^3)^2
={(1111)*g}^2
∴(1 234 321)*g是(1111)*g的平方式