MIPS Assembly Language Programming

4 CHAPTER 1. DATA REPRESENTATION
length n are used, starting from zero, the largest number will be 2 n − 1.
1.1.1.2 Conversion of Decimal to Binary
An algorithm for converting a decimal number to binary notation is given in algorithm
1.2.
Algorithm 1.2 To convert a positive decimal number to binary.
• Let X be an unsigned binary number, n digits in length.
• Let D be a positive decimal number, no larger than 2 n − 1.
• Let i be a counter.
1. Let X = 0 (set all bits in X to 0).
2. Let i = (n − 1).
3. While i ≥ 0 do:
(a) If D ≥ 2 i , then
• Set Xi = 1 (i.e. set bit i of X to 1).
• Set D = (D − 2 i ).
(b) Set i = (i − 1).
1.1.1.3 Addition of Unsigned Binary Numbers
Addition of binary numbers can be done in exactly the same way as addition of
decimal numbers, except that all of the operations are done in binary (base 2) rather
than decimal (base 10). Algorithm 1.3 gives a method which can be used to perform
binary addition.
When algorithm 1.3 terminates, if c is not 0, then an overflow has occurred– the
resulting number is simply too large to be represented by an n-bit unsigned binary
number.