Binary Table 0–100: Decimal, Octal, and Hex Chart

A binary table is a fast reference for matching a decimal number to its base-2 representation. The chart below covers 0 through 100 and adds octal and hexadecimal so you can compare the same value across the four most common positional number systems.

Use your browser's find command to jump to a decimal or binary value. For an interactive result with calculation steps, open the decimal to binary converter or binary to decimal converter.

Binary Conversion Table from 0 to 100

How to Read the Binary Table

Each row represents one mathematical value written in four bases:

• Decimal uses ten digits, 0 through 9.
• Binary uses 0 and 1.
• Octal uses 0 through 7.
• Hexadecimal uses 0 through 9 and A through F.

For example, the row for decimal 42 shows binary 101010, octal 52, and hexadecimal 2A. These strings look different, but they describe the same quantity.

The binary column does not include leading zeros because this table records values rather than fixed-width storage. If you need eight-bit formatting, pad the binary value on the left: decimal 5 is 101 as a value and 00000101 in an eight-bit field.

Patterns Visible in a Binary Number Chart

The binary table exposes several useful patterns.

Powers of Two Add a New Position

At 1, 2, 4, 8, 16, 32, and 64, the binary form is a 1 followed by zeros:

A power of two begins a new bit width. The preceding value contains all 1s: 7 is 111, 15 is 1111, 31 is 11111, and 63 is 111111.

Even and Odd Values

Every even number ends in binary 0 because it contains no 2⁰ contribution. Every odd number ends in binary 1. This gives an immediate parity check without converting the full value.

Three Bits Map to Octal

Each octal digit corresponds to exactly three binary digits. Group 101010 from the right as 101 010; those groups map to octal 5 and 2, producing 52.

Use the binary to octal converter for longer values and grouping steps.

Four Bits Map to Hexadecimal

Each hexadecimal digit corresponds to four binary digits. Pad and group 101010 as 0010 1010; the groups map to hexadecimal 2 and A, producing 2A.

Use the binary to hexadecimal converter when you want the grouped calculation.

Common Binary Table Ranges

4-Bit Binary Table

Four bits provide (2^4 = 16) patterns, covering unsigned decimal 0 through 15. The largest value is 1111, which maps to hexadecimal F. This range is one complete hexadecimal digit.

8-Bit Binary Table

Eight bits provide 256 patterns, covering unsigned decimal 0 through 255. This page stops at 100, but every listed value fits within one byte. Pad each binary entry to eight digits when byte formatting matters.

An unsigned byte ranges from 00000000 to 11111111. A signed two's complement byte uses the same patterns but interprets them as -128 through 127. A table cannot determine the interpretation without knowing the data type.

Using the Chart to Check Arithmetic

A binary conversion table can verify small additions and subtractions. Find both input values in decimal, perform the familiar decimal operation, and locate the result row.

For example:

Binary:  1011 + 0110 = 10001
Decimal:   11 +    6 =    17

The row for 17 confirms 10001. For visible carry handling, use the binary addition calculator. For borrow steps and negative differences, use the binary subtraction calculator.

Frequently Asked Questions

Is binary 100 equal to decimal 100?

No. Without an explicit base marker, the notation is ambiguous. Binary 100₂ equals decimal 4 because it contains one 2² place. Decimal 100 converts to binary 1100100₂.

Why does the table omit leading zeros?

Leading zeros do not change an integer's mathematical value. The chart uses the shortest form. Add zeros to match a required bit width, such as 00001010 for decimal 10 in an eight-bit field.

What comes after 1111 in binary?

Adding one to 1111 carries through every position and creates 10000, which is decimal 16.

How many values fit in n bits?

Exactly $2^n$ distinct patterns. An unsigned n-bit integer ranges from 0 to $2^n-1$.

Can I use the chart for signed numbers?

The rows show non-negative mathematical values. Signed hardware representations require a specified bit width and encoding, usually two's complement. Read the binary number system guide for the distinction between patterns, unsigned range, and signed interpretation.