1. Lecture 6 Excess Notation

2. Excess 8 notation indicates that the value for zero is the bit pattern for 8, that is 1000 Excess 8 notation indicates that the value for zero is the bit pattern for 8, that is 1000 The bit patterns are 4 bits long The bit patterns are 4 bits long Positive numbers are above it in order and negative numbers are below it in order. Positive numbers are above it in order and negative numbers are below it in order.

3. Figure 1.24 An excess eight conversion table

4. Excess Notation (continue) That is the zero point for Excess 128 notation is 128; the zero point for excess 64 notation is 64; and so forth. That is the zero point for Excess 128 notation is 128; the zero point for excess 64 notation is 64; and so forth. For example, let's say we want to determine the pattern for 15 in Excess 128 notation. For example, let's say we want to determine the pattern for 15 in Excess 128 notation. The decimal number would be 128 + 15, or 143. Therefore, the bit pattern would be 10001111. The decimal number would be 128 + 15, or 143. Therefore, the bit pattern would be 10001111.

5. Excess Notation Formulas

6. Example1 A computer stores decimal integer values in 8 bits, using excess-128 notation. How would the decimal value -60 stored? A computer stores decimal integer values in 8 bits, using excess-128 notation. How would the decimal value -60 stored? Solution: Solution: stored number = -60 + 128 stored number = -60 + 128 = 68 10 (1000100 2 ) = 68 10 (1000100 2 )

7. Example 2 The binary number, 0101 1101, is in excess-128 notation. What is the number in decimal? The binary number, 0101 1101, is in excess-128 notation. What is the number in decimal? Solution: Solution: 0101 1101 = 0*128 + 64 + 0*32 + 16 +8 + 4 + 0101 1101 = 0*128 + 64 + 0*32 + 16 +8 + 4 + 0*2 + 1 0*2 + 1 = 93 in excess-128 = 93 in excess-128 actual number = 93 – 128 = -35 actual number = 93 – 128 = -35