Number Systems

Binary to Decimal Conversion

Conversion of binary to decimal (base-2 to base-10) numbers and back is an important concept to understand as the binary numbering system forms the basis for all computer and digital systems.

Examples:

10101₂ = 10101B = 1×2⁴+0×2³+1×2²+0×2¹+1×2⁰ = 16+4+1= 2110111₂ = 10111B = 1×2⁴+0×2³+1×2²+1×2¹+1×2⁰ = 16+4+2+1= 23100011₂ = 100011B = 1×2⁵+0×2⁴+0×2³+0×2²+1×2¹+1×2⁰=32+2+1= 35

Summary

• A “BIT” is the abbreviated term derived from BInary digiT
• A Binary system has only two states, Logic “0” and Logic “1” giving a base of 2
• A Decimal system uses 10 different digits, 0 to 9 giving it a base of 10
• A Binary number is a weighted number who’s weighted value increases from right to left
• The weight of a binary digit doubles from right to left
• A decimal number can be converted to a binary number by using the sum-of-weights method or the repeated division-by-2 method
• When we convert numbers from binary to decimal, or decimal to binary, subscripts are used to avoid errors