Memory as numbered boxes: bits, bytes, addresses; a variable as a named box

0 · Recall Warm-up

Answer from memory first. Answers are in the Answer Vault at the bottom.

• What does the compiler produce when your source code has no errors? from Lesson 0.1.1
• How many characters does "\n\n" contain? from Lesson 0.1.1
• Where does every C program start running? from Lesson 0.1.1

1 · The Hook

🎣

A shopkeeper adds up a bill: price 40, quantity 3, total 120. While working, she writes each number on a slip and keeps the slips in labelled trays: “price”, “quantity”, “total”. When the quantity changes, she crosses out the old number in that tray and writes the new one.

A program needs the same thing: places to keep numbers while it runs, each with a label, each able to change. This lesson shows what those places are inside a computer.

2 · Predict First

🤔

What does this print?

int a = 3;
int b = 4;
a = b;
b = a;
printf("%d %d\n", a, b);

Make a guess in your head. The answer opens Section 3.

3 · Core Concept

💡

Predict First — the answer

Output

4 4

a = b; copies 4 into a, and the old 3 is gone for ever. Then b = a; copies that 4 back into b. Assignment overwrites; it never swaps.

Bits

A bit is the smallest piece of information: a single 0 or 1, like a switch that is off or on. One bit has 2 possible patterns. Two bits have 4 (00, 01, 10, 11). Three bits have 8. Each extra bit doubles the number of patterns, because every old pattern can be followed by a 0 or by a 1.

Bytes

A byte is a group of 8 bits. Doubling 8 times from 1 gives 256, so one byte has 256 possible patterns. Memory sizes and data sizes are counted in bytes.

Memory: numbered boxes

The computer’s main memory is a very long row of boxes, each holding one byte. Every box has a number, its address, starting from 0. To read or change a byte, the processor names its address.

A value that needs more than one byte occupies several consecutive boxes. Its address is the address of its first byte.

A variable is a named box

A variable is a named piece of memory that holds a value which can change. In C you must say what kind of value it holds before using it:

int count;

This asks for a box big enough for one whole number (int). On the machine these notes assume, an int takes 4 bytes, so count occupies 4 consecutive addresses, say 1000 to 1003, and its address is 1000. You use the name; the compiler keeps track of the address.

Assignment: store, then forget the old value

x = 5; means “store 5 in the box called x”. The old content is overwritten. The right side is worked out first, using the current values, and only then stored. That is why

x = x + 1;

makes sense: read x, add 1, store the result back into x. The = sign in C means store, not “is equal to”.

Giving a first value

int x = 5; creates the box and stores 5 in it straight away. If you create a variable inside main without a first value (int y;) its box holds whatever bits were left there before: an unpredictable value. Using it before storing something is a bug.

Printing a variable

Inside the string literal given to printf, the pair %d is a placeholder: it is replaced by the value of the next item after the string, written as a whole number. Several placeholders are filled in order:

printf("%d %d\n", a, b);   /* first %d gets a, second gets b */

Naming rules

A name (an identifier) may use letters, digits and the underscore _, must not start with a digit, and must not be a word C reserves for itself (a keyword such as int or return). Names are case-sensitive: total and Total are different variables.

4 · Visual

int x = 5; int y = 9; — each int uses four consecutive one-byte boxes. The address of x is 1000, the address of y is 1004 (addresses chosen for the picture; the real ones depend on the machine).

Trace of:  int a = 3;  int b = 4;  int t;  t = a;  a = b;  b = t;

statement      a     b     t
-----------    ---   ---   ---
int a = 3;      3     -     -
int b = 4;      3     4     -
int t;          3     4     ?      <- unpredictable until stored
t = a;          3     4     3
a = b;          4     4     3
b = t;          4     3     3      -> prints "4 3"

A trace table: one row per statement, one column per variable, showing the state after the statement runs.

5 · Worked Examples

Example 1 Easy

What does this print?

int x = 5;
x = 8;
x = x + 2;
printf("%d\n", x);

Solution

x = 5, then 8 (5 is gone), then 8 + 2 = 10.

Output

10

Example 2 Medium

What does this print?

int p = 2;
int q = p + 3;
p = q + p;
q = p - q;
printf("p = %d, q = %d\n", p, q);

Solution

Output

p = 7, q = 2

Each right side uses the values at that moment: in the last line p is already 7.

Example 3 GATE

Swap the values of a (3) and b (4). Why does a = b; b = a; fail, and what fixes it?

Solution

The first assignment destroys a’s old value, so both end as 4 (the Predict First question). Keep a copy in a third box first:

int a = 3;
int b = 4;
int t;
t = a;
a = b;
b = t;
printf("%d %d\n", a, b);

Output

4 3

The trace table in the Visual section shows every step.

6 · GATE Traps

⚠️

• = stores; it is not a question. a = b copies b into a and destroys a’s old value.
• The right side is computed with the values before the store: in p = q + p the old p is used.
• A multi-byte value’s address is the address of its first byte; an int at 2000 also occupies 2001, 2002 and 2003.
• A variable created without a first value holds an unpredictable value; never print or use it before storing.
• Names are case-sensitive and cannot start with a digit: 2nd is not a valid name; _count is.

8 · Memory Hook

🧠

Bit = switch, byte = 8 switches, address = house number, variable = a named house. Assignment is moving in a new tenant: the old one is gone for good.

9 · Connect the Dots

Lesson 0.1.1 printed fixed text; now values live in named boxes and %d prints them. Each extra bit doubled the number of patterns, and memory sizes keep growing by doubling. Next lesson answers: how do we write and work with “2 multiplied by itself many times”, and how many halvings does it take to shrink a number to 1?

10 · Self-Test

GATE format. Try every question before opening the vault.

Q1MCQ1 markOutput

What does this print?

int x = 1;
int y = 2;
int z = 3;
x = y + z;
y = x + z;
z = x + y;
printf("%d %d %d\n", x, y, z);

• (A) 5 8 13
• (B) 1 2 3
• (C) 5 5 8
• (D) 5 7 10

Q2NAT1 markAddresses

An int (4 bytes) starts at address 2000. What is the address of its last byte?

Numerical answer: ________

Q3MSQ1 markIdentifiers

Which are valid variable names in C?

• (A) total_marks
• (B) 2ndPlace
• (C) return
• (D) _x1

Q4NAT1 markBits

How many different patterns can 5 bits hold?

Numerical answer: ________

Q5MCQ2 marksOutput

What does this print?

int n = 10;
n = n + n;
n = n + n;
printf("%d\n", n);

• (A) 30
• (B) 10
• (C) 20
• (D) 40

11 · Rule Card

• bit = 0 or 1; byte = 8 bits; n bits → patterns double with each bit (8 bits → 256).
• Memory = numbered one-byte boxes; number = address; multi-byte value’s address = its first byte.
• int = whole number, 4 bytes here; int x = 5; creates and fills a box.
• x = expr; evaluate right side with current values, then overwrite x.
• Unfilled local variable = unpredictable value.
• %d in printf = placeholder for the next value, as a whole number.
• Identifier: letters, digits, _; not starting with a digit; not a keyword; case-sensitive.
• Swap needs a third variable: t = a; a = b; b = t;

12 · Concept Ledger

Unlocked in this lesson. From here on, these terms may be used.

bitbytememoryaddressvariableint (4 bytes here)assignment =first value (initialization)unpredictable value of an unfilled variable%d placeholderidentifierkeywordtrace table

13 · Answer Vault