UPC EETAC Bachelor's Degree in Telecommunications Systems and in Network Engineering EEL


Lecture 1

L3.1: Arithmetics in radix-2

[P3] Binary codes and radix-2 adders, comparators and  multipliers



1.8. Binary codes and code converters

1.8.1. Number systems. Binary radix 2 (base 2), octal (base 8, hexadecimal (base 16)

number system


1.8.2. Gray code


1.8.3. BCD (binary-coded decimal)


1.8.4. One-hot and one-cold


1.8.5. Johnson


1.8.6. Keyboard symbols: ASCII, etc.


 1.8.7. Code converter circuits Bin_BCD_converter_6bit Gray_Bin_converter_4bit

1.9. Binary (radix-2, base-2) arithmetic circuits

1.9.1. Addition 1-bit adder (Adder_1bit)

Binary numbers, symbols, range and how to perform additions.


Conversion from binary to decimal, decimal to binary. Hexadecimal numbers. How to use the computer calculator in programming mode to work with bin/hex/oct/dec numbers.

PC calculator in mode programmer

Planning 1-bit expandable adders: tutorials on how to design the 1-bit full adder using our plans:

- Plan A: structural (equations)  Adder_1bit

- Plan B: behavioural Adder_1bit

- Plan C2: Hierarchical multiple-file Adder_1bit

1.9.2. Comparator Expandable 1-bit comparator (Comp_1bit)

Symbol and truth table.

Symbol Truth table

Planning expandable comparators:

- Plan A: 1-bit expandable comparator Comp_1bit 

- Plan B: 1-bit expandable comparator Comp_1bit 

- Plan C2: 1-bit expandable comparator Comp_1bit using the MoM


1.9.3. Multiplier 1-bit multiplier cell, Mult_1bit