Unsigned binary representation
Use place values to convert numbers and preserve a requested bit width.
What you will learn
- Convert a non-negative denary integer to binary.
- Explain leading zeros and the range of an unsigned byte.
Binary uses powers of two
Each binary digit is 0 or 1. Starting on the right, place values are 1,2,4,8,16,32,64,128. A one includes that place value and a zero excludes it. Add the included values to convert binary to denary.
For conversion in the other direction, work from the largest place value downward. If that value fits into the remaining amount, write one and subtract it; otherwise write zero.
Value and format both matter
Leading zeros do not change an unsigned binary value, but they do affect the written width. An instruction requesting eight bits requires eight digits. The largest unsigned eight-bit value is 255 and the smallest is zero.
Signed representations use a different interpretation. Do not apply an unsigned conversion rule to two's-complement numbers without considering the sign bit.
Worked example
Convert denary 53 into unsigned eight-bit binary.
Show the worked solution
- 53 contains 32, leaving 21; include 16, leaving 5.
- Include 4 and 1, giving 32+16+4+1.
- For places 128,64,32,16,8,4,2,1, write 0,0,1,1,0,1,0,1.
Answer 00110101
Common mistakes
- A correct value can still have the wrong requested width.
- Each place is a power of two, not a power of ten.
What can you explain now?
Convert 00011010 to denary.
Compare with the explanation
26
The set bits represent 16+8+2.
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