###### Asked in EngineeringElectrical EngineeringNumbers

Engineering

Electrical Engineering

Numbers

# What is the base 10 value for the binary number 1101?

## Answer

###### Wiki User

###### August 06, 2008 9:21PM

Let's give a simple answer and explanation:

1101 = 1000 + 100 + 1 [binary]

= 8 + 4 + 1 [decimal]

8 + 4 + 1 = 13 [decimal]

## Related Questions

###### Asked in Computer Programming

### What is 01001001001000000110110001101111011101100100101001000000111100101 in binary code?

N = 1001 0010 0100 0000 1101 1000 1101 1110 1110 1100 1001 0100
1000 0001 1110 0101
If N is already in binary and you want to convert it to our
normal base-10 system, then the value would be:
10,538,661,580,010,455,525
If N is already in base-10 and you want to convert it to binary,
then the value would be:
0010 0110 1110 1110 1100 1010 1000 1110 0110 1101 1111 1100 0011
0100 1111 1110 1101 1101 1111 0101 1110 1000 1000 1101 1110 0100
0011 1001 1011 1001 0101 0001 0010 1010 0100 0111 0000 1100 0010
0101 0110 1010 1010 1011 1011 1101 1000 0101 1001 1100 0000 1100
0101

###### Asked in Math and Arithmetic

### How do you multiply a number by two in base two?

Just add a zero on the right-hand end of it.
==============================
Another contributor bloviated:
Just the same as multiplying a number in base ten by ten : just
tack a 0 on the end,
Binary 11 (decimal value 3) multiplied by decimal two is binary
11 times binary 10 which comes to binary 110.
In any base, multiplying by the value of the base tacks a zero
on the end, because the value of the base, written in that base, is
always 10.

###### Asked in Math and Arithmetic, Numbers

### How is a binary number converted to a decimal number?

This is done in the same manner of converting a number in any
non-decimal base (not base 10) to a decimal (base 10) number:
In each base system, the place value columns are the base times
bigger than the column to its right.
The column before the base-point is the units or ones column.
The next column left is the 1 × base = base column, the next column
left is the base × base = base² column and so on.
To convert the number, sum each each digit of the base
multiplied by its place value column.
For base 2, the place value columns (left from just left of the
binary-point) are 1, 2, 2² = 4, 2³ = 8, 16, 32, ...
As a binary number only has 1s and 0s, converting a binary
number to decimal is simply adding together the value of the place
value columns that have a 1.
eg 101101₂ = 32 × 1 + 16 × 0 + 8 × 1 + 4 × 1 + 2 × 0 + 1 × 1 =
32 + 8 + 4 + 1 = 45

###### Asked in Math and Arithmetic, Percentages, Fractions, and Decimal Values

### Why is it so difficult to convert a number from decimal to binary?

I can't say for certain what your specific difficulty is with
the process, so I will guess unfamiliarity. There are many fine
websites that will perform those calculations automatically.
------------------------------
There is a general method to convert from base 10 to any other
base:
divide the number by the base to get a whole number quotient
and remainder
note the remainder
replace the number by the quotient
if the number is not zero repeat from step 1
write the remainders in reverse order to get the decimal number
in the new base.
With this converting a decimal number to binary is quite
straight forward; for example 205 in binary:
205 ÷ 2 = 102 r 1
102 ÷ 2 = 51 r 0
51 ÷ 2 = 25 r 1
25 ÷ 2 = 12 r 1
12 ÷ 2 = 6 r 0
6 ÷ 2 = 3 r 0
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1
→ 205 in decimal is 1100 1101 in binary.
What you may be complaining about is that converting octal and
hexadecimal numbers to binary is extremely straight forward and
direct; examples:
0315 (octal) = 11 001 101 = 1100 1101 in binary
0xcd (hexadecimal) = 1100 1101 binary
These conversions are extremely easy as each digit of an octal
or hexadecimal number uses an exact number of binary digits:
octal numbers 0-7 are the fill range of the binary numbers
000-111 - 3 binary digits
hexadecimal numbers 0-f are the full range of the binary numbers
0000-1111 - 4 binary digits.
There is no waste so each digit of an octal or hexadecimal
number can be converted into binary directly. Each new octal or
hexadecimal place value column is represented by an exact 3 or 4
block of binary digits, so when a place value is added, another
block of binary digits is added, so 07 + 01 = 010 which in binary
is 111 + 001 = 001 000; similarly 0xf + 0x1 = 0x10 which in binary
is 1111 + 0001 = 0001 0000
With decimal numbers, however, the digits 0-9 are represented by
the binary 0000-1001; if each digit of a decimal number was
converted to binary (an encoding known as Binary Coded Decimal, or
BCD) then the binary numbers 1010-1111 (6 of them) are not being
used and wasted. Alternatively, when a new place value is needed in
decimal the binary will still likely use the binary digits already
being used without the need for an extra block, eg 9 + 1 = 10 which
in binary is 1001 + 0001 = 1010; there is no 1:1 correspondence
between blocks of binary digits and decimal digits that occurs with
octal and hexadecimal numbers.

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