Binary & Hexadecimal
Teens & adults Computing Number systems
Decimal is base 10: each digit worth 10× the one to its right. Binary is base 2 — only 0 and 1 — because a transistor is either off or on. Hexadecimal (hex) is base 16: digits 0–9 plus A–F for 10–15.
Reading binary
binary 1 0 1 1
values 8 4 2 1 ← powers of 2
1·8 + 0·4 + 1·2 + 1·1 = 8 + 2 + 1 = 11 in decimal
Hex is binary in disguise
One hex digit = exactly 4 binary bits. That's why programmers use it — compact but instantly convertible:
$FF = 1111 1111 = 255
$A0 = 1010 0000 = 160 (A = 10, then 0)
$FF3300 = a 24-bit color: FF red, 33 green, 00 blue
Converting decimal → binary
Repeatedly halve, keep the remainders, read bottom-up:
13 → 6 r1 → 3 r0 → 1 r1 → 0 r1 → reads
1101 = 13.
In ALB
ALB source accepts
$FF3300 hex colors and
0x04 C-style hex — this is the math underneath both.
Practice
Binary 1101 in decimal = ___
Hex $FF in decimal = ___
Decimal 10 in binary = ___ (digits only)
One hex digit represents how many binary bits?
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