BIN2DEC

 The BIN2DEC function in Excel is used to convert a binary number (base-2) to its decimal equivalent (base-10). Below is an explanation of how the function works, including examples with data and formulas.

---

Syntax

excel

Copy

BIN2DEC(number)

• number: The binary number you want to convert to decimal. It can be up to 10 characters (bits) long. The most significant bit (leftmost bit) represents the sign (0 for positive, 1 for negative).

---

Key Points

1. The binary number must be a string of 0s and 1s.

2. If the binary number is negative (starts with 1), the result will be a negative decimal number.

3. If the binary number is longer than 10 characters, BIN2DEC will return a #NUM! error.

---

Examples

Example 1: Positive Binary Number

• Binary Number: 1010 (which is 10 in decimal)

• Formula: =BIN2DEC("1010")

• Result: 10

---

Example 2: Negative Binary Number

• Binary Number: 1111111110 (which is -2 in decimal)

• Formula: =BIN2DEC("1111111110")

• Result: -2

---

Example 3: Binary Number Longer Than 10 Bits

• Binary Number: 10101010101 (11 bits)

• Formula: =BIN2DEC("10101010101")

• Result: #NUM! (error because the binary number exceeds 10 bits)

---

Step-by-Step Explanation

1. Positive Binary Number:

   • Binary: 1010

   • Calculation:

     Copy

     1 * 2^3 = 8
     0 * 2^2 = 0
     1 * 2^1 = 2
     0 * 2^0 = 0
     -----------------
     Total = 8 + 0 + 2 + 0 = 10

   • Result: 10

2. Negative Binary Number:

   • Binary: 1111111110

   • The leftmost bit is 1, so it represents a negative number.

   • To convert:

     • Invert the bits: 0000000001

     • Add 1: 0000000010 (which is 2 in decimal)

     • Apply the negative sign: -2

   • Result: -2

---

Excel Table Example

Binary Number	Formula	Decimal Result
1010	=BIN2DEC(A2)	10
1111111110	=BIN2DEC(A3)	-2
10101010101	=BIN2DEC(A4)	#NUM!

---

Notes

• If you need to convert binary numbers longer than 10 bits, you can use a custom formula or break the number into smaller parts.

• For positive numbers, the leftmost bit must be 0.

• For negative numbers, the leftmost bit must be 1, and the number is represented in two's complement form.