Cambridge O Level Computer Science · Syllabus 2210 · Data Representation
Place Value
What is Place Value?
Place value is the worth attached to a digit because of the column it occupies, where each column is worth the base times the column to its right — powers of 2 in binary and powers of 16 in hexadecimal.
This definition is part of the Data Representation chapter in Cambridge O Level Computer Science.
Place Value in context
Every form of data a computer handles — a number, a character, a sound, an image — is converted into binary before it can be processed or stored. The conversion is done by an agreed encoding rule: place value for numbers, a character set for text, sampling for sound, pixels and colour depth for images. The binary is then held in fixed-width registers and processed using logic gates. Nothing about the pattern 01000001 tells you whether it means the number 65, the character A, one sample of a sound or one pixel of an image — only the rule you were told to apply does.
Two's complement is the standard way of representing negative numbers in binary. In an 8-bit two's-complement number the leftmost column is given the place value −128 instead of +128; every other column keeps its usual positive value. That single change lets one 8-bit pattern represent any integer from −128 to +127. A positive value has a most significant bit of 0; a negative value has a most significant bit of 1.
Common mistakes with Place Value
- 4. Reading the most significant bit as a minus sign. Why it fails In two's complement the leading 1 is not a sign symbol attached to the rest; it is a place value of −128. Reading 11010011 as "minus 1010011" gives −83. The correct value is −45. Fix Either use the signed place values with −128 at the left, or invert and add 1. See section 1.1 H.
- M8. "The most significant bit is simply a minus sign." Why it fails In two's complement the leading 1 is a place value of −128 that is added to the rest — it is not a symbol you can detach and ignore. Correct model Read 11010011 as −128 + 64 + 16 + 2 + 1 = −45, not as "minus 1010011" = −83. Exam-safe "In two's complement the most significant bit has a place value of −128; a leading 1 indicates a negative number but the other bits still add positive values to it." Test yourselfHideQ. What denary value is the two's-complement pattern 11111111?A. −1, not −127.
Questions students ask about Place Value
How do you read a negative number stored in two's complement?
In an 8-bit two's complement number the leftmost (most significant) bit has a place value of −128 instead of +128; every other column keeps its usual positive value. Read the pattern by adding the place values of every 1 bit, including the negative one. For example, 11010011 is −128 + 64 + 16 + 2 + 1 = −45 — not "minus 1010011", which would wrongly give −83. This lets one 8-bit pattern represent any integer from −128 to +127, with a single representation of zero.