# Midterm 2 -- 9 November, 1995

## Problem 1. (8 points)

Convert the decimal number 107 into a binary number.

## Problem 2. (8 points)

Convert the binary number 10010110 into a decimal number.

## Problem 3. (14 points)

Represent the following decimal numbers as twelve-bit two's complement binary numbers.

• 1700
• -102

## Problem 4. (15 points)

Convert the decimal number 17.3 into a floating point number with one sign bit, an eight-bit exponent expressed using excess-127 notation, and a 23-bit mantissa.

## Problem 5. (15 points)

Represent the following PASCAL statement in register transfer language:

```          IF (NOT c) THEN
X := T + 3
ELSE IF (b) THEN
X := T
```

## Problem 6. (15 points)

If registers X and Y have the following values:

• X = 0011110011
• Y = 1111100000

what are their values after each of the following RTL statements are performed

• X <- Y+1, Y <- Y-1
• Y <- cir X

cir is circular shift right.

## Problem 7. (25 points)

Show the hardware needed to implement the following RTL statements for sixteen-bit registers X and Y:

• s : X <- Y, Y <- X
• s' t : X <- X+1, Y <- Y-1

You may use sixteen-bit adders, sixteen-bit multiplexers, sixteen-bit registers and assorted logic gates in your solution.

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