Binary Representation

Part of the Fundamentals section of Coddy's Verilog journey — lesson 13 of 90.

In Verilog, we work with digital circuits that understand only 0 and 1. These are represented in binary.

Binary uses only two digits: 0 and 1. Each binary digit is called a bit.

Decimal	Binary	Bits
0	0	1 bit
1	1	1 bit
2	10	2 bits
3	11	2 bits
4	100	3 bits
5	101	3 bits

Writing Binary in Verilog

To write binary numbers in Verilog, use the prefix 'b:

4'b1010    // 4-bit binary 1010 (decimal 10)
8'b11110000 // 8-bit binary 11110000 (decimal 240)
2'b01      // 2-bit binary 01 (decimal 1)

The number before 'b tells Verilog how many bits the value has.

How to Convert Decimal to Binary

Divide the decimal number by 2 repeatedly and read the remainders from bottom to top.

Example: Convert 9 to binary

Step	Division	Quotient	Remainder
1	9 ÷ 2	4	1
2	4 ÷ 2	2	0
3	2 ÷ 2	1	0
4	1 ÷ 2	0	1

Read remainders from last to first: 1001

9 = 4'b1001

Example in Code

module binary_example;
  reg [3:0] a;
  
  initial begin
    a = 4'b1010;     // Binary 1010 = decimal 10
    $display("a = %b (binary)", a);
    $display("a = %d (decimal)", a);
    $display("a = %h (hex)", a);
    $finish;
  end
endmodule

Output:

a = 1010 (binary)
a = 10 (decimal)
a = a (hex)

Challenge

Complete the code by writing the missing binary values.

What to do:

Write binary for decimal 5 (4 bits)
Write binary for decimal 14 (4 bits)

Cheat sheet

Binary uses only 0 and 1. Each digit is a bit.

Write binary in Verilog with the 'b prefix — the number before it specifies the bit width:

4'b1010    // 4-bit binary = decimal 10
8'b11110000 // 8-bit binary = decimal 240

Display formats: %b (binary), %d (decimal), %h (hex).

Decimal to binary: divide by 2 repeatedly, read remainders bottom to top.

// 9 ÷ 2 → 4 r1 → 2 r0 → 1 r0 → 0 r1  ⟹  1001
// 9 = 4'b1001

Try it yourself

module binary_challenge;
  reg [3:0] a, b;
  
  initial begin
    // Write binary for decimal 5 (4 bits)
    a = 4'b______;
    
    // Write binary for decimal 14 (4 bits)
    b = 4'b______;
    
    $display("5 = %b", a);
    $display("14 = %b", b);
    $finish;
  end
endmodule