Number Bases
The Arithmetic and Logical Unit (ALU) and related operations. ALU can add, subtract, multiply and divide numbers.
The number of digits in a particular number system is called the BASE.
The four (4) numbering system commonly used with micro computer are the binary, octal, decimal and hexadecimal. The binary numbering system uses only two digits i.e. zero (0) and one (1). The octal numbering system is the base 8 numbering system and the digits involved are 0,1,2,3,4,5,6 and 7.
The decimal numbering system is the base 10 numbering system. The digit involved are 0,1,2,3,4,5,6,7,8 and 9.
The hexadecimal or the base 16 numbering system has sixteen digit namely 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. The letter A,B,C,D,E,F represent the natural numbers i.e. 10, 11, 12, 13, 14, 15 respectively. The base written as a subscript and enclosed in bracket. For example the 1101(2), 6573(8), 8963(10) and 63AD (16) are written in the base 2, 8, 10 and 16 respectively.
Conversion of Numbers in base (2) to number is base (10)
2000 + 400 + 50 + 6
i.e. (2 * 1000) + (4 * 100) + (5 * 10) + (6 * 1)
i.e. (2 * 103) + (4 * 102) + (5 * 101) + (6 * 100)
Note that the value of a number raised to power zero is one. I.e. 100 =1,20 =1, 80 =1 etc.
For example, the expanded form of the number 1101(2) then become (1 * 23) + (1 * 22) + (0 *21) + (1 * 20). To convert a number in base 2 to a number in base 10(ten), we simply write the given base 2 number in an expanded form and solve the problem.
Solve the following examples
Convert the following base 2 number to base 10(ten).
A. 1101(2) B. 11111(2) C. 110111(2)
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