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M16_2_Discussion1

M16_2_Discussion1 - Number Systems Binary radix-r = 2...

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Number Systems Binary, radix-r = 2 Quaternary, r = 4 Octal, r = 8 Decimal, r = 10 x = from i=0 to n-1 ∑x i r i x 10 = 7*10 3 + 3*10 2 + 2*10 1 + 2*10 0 = (7322) 10 (47) 10 = (101111) 2 2 6 = 64 2 5 = 32 2 4 = 16 2 5 + 2 3 + 2 2 + 2 1 + 2 0 = 47 47/2 = 23 R 1 23/2 = 11 R 1 11/2 = 5 R 1 5/2 = 2 R 1 2/2 = 1 R 0 Begin last 1 plus last remainder, plus other remainders in reverse order = 101111 47/16 = 2 R 15 2/16 != x 2 15 = 2F 47/8 = 5 R 7 = 57 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 10 (A) 1010 11 (B) 1011 12 (C) 1100 13 (D) 1101 14 (E) 1110 15 (F) 1111

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(B657) 16 = (46679) 10 11*16 3 + 6*16 2 + 5*16 1 + 7*16 0 = 46679 Representing time in binary 24:60:60 60 = 6 bits 24 = 5 bits 13:40:04 01101 : 101000 : 000100 13*60*60 + 40*60 + 4 = 49204 seconds 2 15 + 2 14 + 2 5 + 2 4 + 2 2 = 49204 1100000000110100 Decimals (0.15625) 10 = (?) 2 IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754) A single-precision binary floating-point number is stored in 32 bits. Sign bit (1 bit), exponent (8 bits in IEEE standard), fraction (23 bits in IEEE standard) Ex. 0.15625 Sign bit = 0 Fraction = 0.15625 * 2 = 0.3125 bit 0 0.3125 * 2 = 0.625 bit 0 0.625 * 2 = 1.25 bit 1 0.25 * 2 = 0.5 bit 0 0.5 * 2 = 1.0 bit 1 So you have 0. 00101, now add exponent 2 0 Move 1 to left of decimal without changing value = 1.01 * 2 -3
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M16_2_Discussion1 - Number Systems Binary radix-r = 2...

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