Hex and Powers of Two.pdf - Powers of Two and Hexadecimal Numbers Powers of two 20 = 1 25 = 32 210 = 1024 = 1K(kilo 1 6 2 = 2 2 = 64 220 = 1M(mega 22 =

# Hex and Powers of Two.pdf - Powers of Two and Hexadecimal...

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Powers of Two and Hexadecimal Numbers Powers of two 2 0 = 1 2 5 = 32 2 10 = 1024 = 1K (kilo) 2 1 = 2 2 6 = 64 2 20 = 1M (mega) 2 2 = 4 2 7 = 128 2 30 = 1G (giga) 2 3 = 8 2 8 = 256 2 40 = 1T (tera) 2 4 = 16 2 9 = 512 Rule: 2 m+n = 2 m ´ 2 n Useful examples: 2 16 = 2 10 ´ 2 6 = 1K * 64 = 64K 2 32 = 2 30 ´ 2 2 = 1G * 4 = 4G Logarithms (base 2) log 2 1 = 0 log 2 32 = 5 log 2 1024 = log 2 1K = 10 log 2 2 = 1 log 2 64 = 6 log 2 1M = 20 log 2 4 = 2 log 2 128 = 7 log 2 1G = 30 log 2 8 = 3 log 2 256 = 8 log 2 1T = 40 log 2 16 = 4 log 2 512 = 9 Rule: log 2 (m ´ n) = log 2 m + log 2 n Useful examples: log 2 16M = log 2 16 + log 2 1M = 4 + 20 = 24 log 2 32G = log 2 32 + log 2 1G = 5 + 30 = 35 In a computer system, an n-bit memory location can store one of 2 n different numbers. Example: A 32-bit variable can store any of 2 32 different numbers. In a computer system, an n-bit address can refer to any of 2 n different memory locations. Example: A