What is 7 as a 4-bit binary number?
Understand the Problem
The question is asking for the binary representation of the decimal number 7 using 4 bits. To represent numbers in binary, we convert the decimal number to binary format. For 7, the binary equivalent in a 4-bit system is '0111'.
Answer
The binary representation of \(7\) using \(4\) bits is \(0111\).
Answer for screen readers
The binary representation of the decimal number (7) using (4) bits is (0111).
Steps to Solve
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Identify the decimal number
We need to convert the decimal number (7) into binary format. -
Determine the binary bits needed
We are required to represent the number using (4) bits. The range of numbers that can be represented with (4) bits is from (0) to (15). -
Convert decimal to binary
To convert (7) to binary, we repeatedly divide the number by (2) and write down the remainder:- (7 \div 2 = 3) remainder (1)
- (3 \div 2 = 1) remainder (1)
- (1 \div 2 = 0) remainder (1)
Now, we read the remainders in reverse order to get the binary representation, resulting in (111).
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Format to 4 bits
Since the binary representation (111) is (3) bits long, we need to pad it with zeros at the start to make it (4) bits. Thus, the binary representation becomes (0111).
The binary representation of the decimal number (7) using (4) bits is (0111).
More Information
In binary, each bit represents a power of (2). The 4-bit binary number (0111) indicates:
- (0 \times 2^3 = 0)
- (1 \times 2^2 = 4)
- (1 \times 2^1 = 2)
- (1 \times 2^0 = 1)
Adding these up gives us (0 + 4 + 2 + 1 = 7).
Tips
One common mistake is miscounting the bits needed. Always ensure to confirm the number of bits required for representation.
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