recap Each digit is a coefficient of the number base raised to an increasing power. One technique works for all number base conversions. Shortcut conversions: decimal to binary (sum powers of 2) binary to decimal (subtract out powers of 2) octal and binary (1 octal digit = 3 binary digits) hex and binary (1 hex digit = 4 binary digits) Effectively, hex and octal serve as a compacter way of writing binary.
finite rational (rational with a fractional component which can be expressed with a finite number of digits) 3/4 -7/1 138/20 1/3 738/61 0.75 -7.0 6.9 0.33 12.0983606557…
a ratio with denominator 2 a 5 b is finite in decimal a ratio with denominator 2 a is finite in octal a ratio with denominator 2 a is finite in hex a ratio with denominator 2 a is finite in binary all ratios which are finite in binary are also finite in decimal some ratios which are finite in decimal are also finite in binary
rational as two integers 3/4 Numerator: 00000011 Denominator: 00000100 -7/13 Numerator: 11111001 Denominator: 00001101
fixed-point 57/8 111.001b Integer: 00000111 Fraction: 00100000 (the computing equivalent of radix-point notation)