EECS 1520 Lecture Notes - Lecture 3: Scientific Notation, Radix Point, Radix

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1520
• Professor: Steven Castellucci

Document Summary

To store integers, half the cominations are used to represent negative values. The msb is used to represent the sign. The range for integers in 1 byte is: -128 to +127 (cid:1006)"s (cid:272)o(cid:373)ple(cid:373)e(cid:374)t (cid:374)otatio(cid:374) The notation system that uses 1 to represent negative values. The pattern immediately before zero is -1: If each value is stored using 8 bits, then 127 + 3 overflows: (cid:882)(cid:883)(cid:883)(cid:883)(cid:883)(cid:883)(cid:883)(cid:883)+(cid:882)(cid:882)(cid:882)(cid:882)(cid:882)(cid:882)(cid:883)(cid:883)=(cid:883)(cid:882)(cid:882)(cid:882)(cid:882)(cid:882)(cid:883)(cid:882) This overflow error is the result of trying to represent an infinite range in a finite one. Even 64-bit computers cannot operate with all integers because many of them can be represent as 64 bit binary numbers. Floating point storage (8-bit example) in floating point notation, the bit pattern is divided into 3 components: sign (orig value): 0=positive 1=negative exponent: 1xx = negative (move radix left) xx = number of places moved. 0 110 1001 (cid:373)a(cid:374)tissa: i(cid:374)terpret as (cid:862). (cid:1005)(cid:1004)(cid:1004)(cid:1005)(cid:863) in floating point notation the bit pattern is divided into 3.