Decode four binary places
Use powers of two to translate a small binary number.
Supplied materials
- Paper or a note app.
- Four place values, from left to right: 8, 4, 2, 1. A 1 means include that value; a 0 means leave it out. These are unsigned four-bit numbers.
Learn the idea
Decimal place values grow by factors of ten. Binary place values grow by factors of two, and each digit is either 0 or 1. A bit is one binary digit.
The digits are not individual decimal numbers to concatenate. Add the values of the places with a 1. Leading zeros preserve the four-place format without changing the amount.
- Write 8, 4, 2, 1 above four empty places.
- Place 1, 0, 1, 1 underneath them.
- Add only the included values.
- Decode 1101 using the same method.
See the method in action
1011 includes 8, skips 4, and includes 2 and 1. Its decimal value is 8 + 2 + 1 = 11.
Check your reasoning
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See the answer and explanation
13
1101 includes 8 + 4 + 1 = 13 and excludes the 2-place. Reading the characters as the decimal number 1,101 ignores the stated binary place values.
Take it further
Find the four-bit representation of 6. Check: 0110 includes 4 and 2. Then explain why these four unsigned places can represent 0 through 15.
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Longer courses for learners ages 14+
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