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Digital Design

Digital Logic 101.1: Numeric System

Base 10 (a.k.a. decimal) is the numeric system which most people using in daily life.

For the digital logic or computer system in nowadays, it would use binary instead. Binary only have two values, 0 and 1. For any number that larger than one, it should be represented by two digital.

$latex 2_{10} = 10_2$
$latex 5_{10} = 101_2$

A number represented as binary has longer length comparing with decimal. Usually, hexadecimal is used for written down in the program.

$latex 1_{10} = 1_{2} = 1_{16}$
$latex 2_{10} = 10_{2} = 2_{16}$
$latex 3_{10} = 11_{2} = 3_{16}$
$latex 4_{10} = 100_{2} = 4_{16}$
$latex 5_{10} = 101_{2} = 5_{16}$
$latex 6_{10} = 110_{2} = 6_{16}$
$latex 7_{10} = 111_{2} = 7_{16}$
$latex 8_{10} = 1000_{2} = 8_{16}$
$latex 9_{10} = 1001_{2} = 9_{16}$
$latex 10_{10} = 1010_{2} = A_{16}$
$latex 11_{10} = 1011_{2} = B_{16}$
$latex 12_{10} = 1100_{2} = C_{16}$
$latex 13_{10} = 1101_{2} = D_{16}$
$latex 14_{10} = 1110_{2} = E_{16}$
$latex 15_{10} = 1111_{2} = F_{16}$
$latex 16_{10} = 10000_{2} = 10_{16}$

Prefixes is add for represent the binary and hexadecimal in the source code. Here is the example in C.
0x0A

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