Digital Electronics and Design with VHDL

2 Binary Representations

Chapter Contents

2.1 Binary Code

2.2 Octal and Hexadecimal Codes

2.3 Gray Code

2.4 BCD Code

2.5 Codes for Negative Numbers

2.6 Floating-Point Representation

2.7 ASCII Code

2.8 Unicode

2.9 Exercises

Objective:

This chapter shows how bits can be used to represent numbers and characters. The codes presented for integers are sequential binary, octal, hexadecimal, Gray, and BCD. The codes for negative integers are sign-magnitude, one’s complement, and two’s complement. The codes for real numbers are single and double-precision floating-point. And finally, the codes for characters are ASCII and Unicode.

2.1 Binary Code

When we press a number, such as 5, in a calculator’s keypad, two things happen: On one hand, the number ...