Question

Express the following numbers in polynomial form and then calculate the correspondent expression:

a. 1897 in base 10 =

b. 35 in base 12 =

c. 23 in base 4 =

d. 21202 in base 3 =

e. 1101.0111 in base 2 =

Answer 1

a)
=> 1897
=> 1x10^3+8x10^2+9x10^1+7x10^0
=> 1x1000+8x100+9x10+7x1
=> 1x1000+8x100+9x10+7x1
=> 1000+800+90+7
=> 1897

b)
=> 35
=> 3x12^1+5x12^0
=> 3x12+5x1
=> 3x12+5x1
=> 36+5
=> 41

c)
=> 23
=> 2x4^1+3x4^0
=> 2x4+3x1
=> 2x4+3x1
=> 8+3
=> 11

d)
=> 21202
=> 2x3^4+1x3^3+2x3^2+0x3^1+2x3^0
=> 2x81+1x27+2x9+0x3+2x1
=> 2x81+1x27+2x9+0x3+2x1
=> 162+27+18+0+2
=> 209

e)
=> 1101.0111
=> 1x2^3+1x2^2+0x2^1+1x2^0+0x2^-1+1x2^-2+1x2^-3+1x2^-4
=> 1x8+1x4+0x2+1x1+0x0.5+1x0.25+1x0.125+1x0.0625
=> 8+4+0+1+0.0+0.25+0.125+0.0625
=> 13.4375