MIPS Assembly Language Programming

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1.1. REPRESENTING INTEGERS 3 Algorithm 1.1 To convert a binary number to decimal. • Let X be a binary number, n digits in length, composed of bits Xn−1 · · · X0. • Let D be a decimal number. • Let i be a counter. 1. Let D = 0. 2. Let i = 0. 3. While i < n do: • If Xi == 1 (i.e. if bit i in X is 1), then set D = (D + 2 i ). • Set i = (i + 1). Figure 1.2: Examples of Conversion from Binary to Decimal Binary Decimal 00000000 = 0 = 0 = 0 00000101 = 2 2 + 2 0 = 4 + 1 = 5 00000110 = 2 2 + 2 1 = 4 + 2 = 6 00101101 = 2 5 + 2 3 + 2 2 + 2 0 = 32 + 8 + 4 + 1 = 45 10110000 = 2 7 + 2 5 + 2 4 = 128 + 32 + 16 = 176
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.
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