TAILIEUCHUNG - Lecture Introduction to Computer Programming - Lecture 30

The contents of this chapter include all of the following: Can conditionally compile code, can control line numbers and file names reported by compiler, can emit warnings and errors, can define logical regions of source code. | CSC141- Introduction to Computer Programming Teacher: AHMED MUMTAZ MUSTEHSAN Lecture – 30 Thanks for Lecture Slides: C How to Program by Paul Deital & Harvey Deital 6Ed. 1 Revisit Data Representations in C 2 Integer Numbers Integers Internal representations of integers is a simple function of powers of 2. Since the computer only understands a 1 or 0, all values must be converted to base 2 in order to be stored in a computer. For Example, the number 107 stored in binary would look like: The value is calculated by selecting, or not selecting values associated with a power of 2. So, 107 is represented as: 107 = 64 + 32 + 8 + 2 + 1 When storing integers, larger numbers are possible by simply using more bits (2 or 4 byte integers). 27 26 25 24 23 22 21 20 0 1 1 0 1 0 1 1 128 64 32 16 8 4 2 1 3 Real Numbers Real Numbers in the decimal system A real number can be expressed as , for example. Some scientific calculators would use the format * 10 2. Computers typically use something closer to the second form So the Real numbers float or double are more complicated to represent than integers because we need to deal with 4 distinct components. . 4 In Decimal, we would say that * 10 2 consists of the following components: the sign ( - ) the Radix is 10 (base 10) the Exponent is 2 the Mantissa is When representing real numbers, the component parts are: Sign bit indicating whether number is positive or negative. The base or radix for exponentiation which is almost always 2 The exponent to which the base is raised (sometimes this is offset by a fixed number called a bias) The mantissa or significant, an unsigned integer representing the number Real Numbers and their components 5 Float and Double A float in C++ is typically: composed of 32 bits (4 bytes) comprised of: A sign bit. 8 bit exponent (bias of 127) 23 bit mantissa A double in C++ is typically: composed of 64 .

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