Problem: The base of the decimal number system is ten, meaning, for example, that 123=1â‹…102+2â‹…10+3. In the binary system, which has base two, the first five positive integers are 1,10,11,100,101. The numeral 10011 in the binary system would then be written in the decimal system as:
Answer Choices:
A. 19
B. 40
C. 10011
D. 11
E. 7
Solution:
100112​=1⋅24+0⋅23+0⋅22+1⋅21+1⋅20=16+2+1=19.