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**Unformatted text preview: **V 0.1 1 Fixed Point Numbers • The binary integer arithmetic you are used to is known by the more general term of Fixed Point arithmetic. – Fixed Point means that we view the decimal point being in the same place for all numbers involved in the calculation. – For integer interpretation, the decimal point is all the way to the right $C0 + $25-------- $E5 192. + 37.-------- 229. Unsigned integers, decimal point to the right. A common notation for fixed point is ‘X.Y’, where X is the number of digits to the left of the decimal point, Y is the number of digits to the right of the decimal point. V 0.1 2 Fixed Point (cont). • The decimal point can actually be located anywhere in the number -- to the right, somewhere in the middle, to the right $11 + $1F-------- $30 Addition of two 8 bit numbers; different interpretations of results based on location of decimal point 17 + 31-------- 48 xxxxxxxx.0 decimal point to right. This is 8.0 notation. 4.25 + 7.75-------- 12.00 xxxxxx.yy two binary fractional digits. This is 6.2 notation. 0.07 + 0.12-------- 0.19 0.yyyyyyyy decimal point to left (all fractional digits). This is 0.8 notation. V 0.1 3 Algorithm for converting X.Y binary to decimal, decimal to X.Y format. Convert the number 34.7 to its closest representation in 8.4 (12 bit) format: Four bits to right of decimal point, so multiply by 2 4 = 16, truncate 34.7 * 16 = 555.2 = 555 = 0x22B Assume that 0x73A represents a 8.4 (12 bits) fixed point number, what is its decimal representation? Four bits to right of decimal point, so divide by 2 4 = 16 0x73A/16 = 1850 /16 = 115.625. V 0.1 4 Signed X.Y format (2’s complement) Follow the same conversion rules! For –3.25 to 8.4 signed format:-3.25 * 16 = -52 = 0xFCC as a 2’s complement number What is the decimal value of 0xA27 if 8.4 signed format? This is a negative number. Magnitude is: 0x000 – 0xA27 = 0x5D9, so number is –1497. Decimal value is –1497/16 = 93.5625 V 0.1 5 Unsiged Overflow • Recall that a carry out of the Most Significant Digit is an unsigned overflow. This indicates an error - the result is NOT correct! $FF + $01-------- $00 255 + 1-------- 63.75 + 0.25----------- 0 xxxxxxxx.0 decimal point to right xxxxxx.yy two binary fractional digits (6.2 notation) 0.yyyyyyyy decimal point to left (all fractional digits). This 0.8 notation 0.99600 + 0.00391----------- 0 Addition of two 8 bit numbers; different interpretations of results based on location of decimal point V 0.1 6 Saturating Arithmetic • Saturating arithmetic means that if an overflow occurs, the number is clamped to the maximum possible value....

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