MATLAB does not natively display the binary format of numbers. For that, you can use the dec2bin
function, which returns a character vector of binary digits for positive integers. Again, this function
returns only the digits that are not trivially zero.
dec2bin(b)
ans =
'111'
You can use bin2dec to switch between the two formats. For example, you can convert the binary
digits 10110101 to decimal format with the commands
data = [1 0 1 1 0 1 0 1];
dec = bin2dec(num2str(data))
dec = 181
The cast and typecast functions are also useful to switch among different data types. These
functions are similar, but they differ in how they treat the underlying storage of the number:
• cast — Changes the underlying data type of a variable.
• typecast — Converts data types without changing the underlying bits.
Because MATLAB does not display the digits of a binary number directly, you must pay attention to
data types when you work with bit-wise operations. Some functions return binary digits as a
character vector (dec2bin), some return the decimal number (bitand), and others return a vector of
the bits themselves (bitget).
Bit Masking with Logical Operators
MATLAB has several functions that enable you to perform logical operations on the bits of two equallength binary representations of numbers, known as bit masking:
• bitand — If both digits are 1, then the resulting digit is also a 1. Otherwise, the resulting digit is
0.
• bitor — If either digit is 1, then the resulting digit is also a 1. Otherwise, the resulting digit is 0.
• bitxor — If the digits are different, then the resulting digit is a 1. Otherwise, the resulting digit
is 0.
In addition to these functions, the bit-wise complement is available with bitcmp, but this is a unary
operation that flips the bits in only one number at a time.
One use of bit masking is to query the status of a particular bit. For example, if you use a bit-wise
AND operation with the binary number 00001000, you can query the status of the fourth bit. You can
then shift that bit to the first position so that MATLAB returns a 0 or 1 (the next section describes bit
shifting in more detail).
n = 0b10111001;
n4 = bitand(n,0b1000);
n4 = bitshift(n4,-3)
n4 = uint8
1
Bit-wise operations can have surprising applications. For example, consider the 8-bit binary
representation of the number n = 8:
Bit-Wise Operations
2-39
function, which returns a character vector of binary digits for positive integers. Again, this function
returns only the digits that are not trivially zero.
dec2bin(b)
ans =
'111'
You can use bin2dec to switch between the two formats. For example, you can convert the binary
digits 10110101 to decimal format with the commands
data = [1 0 1 1 0 1 0 1];
dec = bin2dec(num2str(data))
dec = 181
The cast and typecast functions are also useful to switch among different data types. These
functions are similar, but they differ in how they treat the underlying storage of the number:
• cast — Changes the underlying data type of a variable.
• typecast — Converts data types without changing the underlying bits.
Because MATLAB does not display the digits of a binary number directly, you must pay attention to
data types when you work with bit-wise operations. Some functions return binary digits as a
character vector (dec2bin), some return the decimal number (bitand), and others return a vector of
the bits themselves (bitget).
Bit Masking with Logical Operators
MATLAB has several functions that enable you to perform logical operations on the bits of two equallength binary representations of numbers, known as bit masking:
• bitand — If both digits are 1, then the resulting digit is also a 1. Otherwise, the resulting digit is
0.
• bitor — If either digit is 1, then the resulting digit is also a 1. Otherwise, the resulting digit is 0.
• bitxor — If the digits are different, then the resulting digit is a 1. Otherwise, the resulting digit
is 0.
In addition to these functions, the bit-wise complement is available with bitcmp, but this is a unary
operation that flips the bits in only one number at a time.
One use of bit masking is to query the status of a particular bit. For example, if you use a bit-wise
AND operation with the binary number 00001000, you can query the status of the fourth bit. You can
then shift that bit to the first position so that MATLAB returns a 0 or 1 (the next section describes bit
shifting in more detail).
n = 0b10111001;
n4 = bitand(n,0b1000);
n4 = bitshift(n4,-3)
n4 = uint8
1
Bit-wise operations can have surprising applications. For example, consider the 8-bit binary
representation of the number n = 8:
Bit-Wise Operations
2-39